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\def\fono{\footnote{}{{\sixrm G.Gaeta - "Geometrical symmetries of nonlinear
equations and physics" - 1/3/93}}}
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\titleaa{A list of references concerning}{Lie-point symmetries of differential equations}
\centerline{Giuseppe Gaeta}
\centerline{Centre de Physique Theorique, Ecole Polytechnique}
\centerline{F-91128 Palaiseau (France)}
\medskip
\centerline{gaeta@orphee.polytechnique.fr}
\centerline{gaeta@roma1.infn.it}
\vskip 3 truecm
{\it What follows is the reference/bibliography section from a volume (maybe) in preparation;
together with a few references concerned with other topics met in the course of the discussion
along the volume, it gives a substantial amount of bibliography for what concerns Lie-point
symmetries of differential equations, in particular for what concerns applications to equations of
interest in Physics and Mathematical Physics; special attention is given to papers published in the
last few years.
I hope the work of collecting this bibliography can be of interest, and maybe even useful, to other
people, so that I put it at disposition of anybody interested in the subject, in the hope I did not
forget or overlook too many contributions; I would be glad of any help in filling the gaps in it.}
\vfill \eject}
\pageno=1
\def\JMP{{\it J. Math. Phys.}}
\def\JPA{{\it J. Phys. A}}
\def\PLA{{\it Phys. Lett. A}}
\def\PRA{{\it Phys. Rev. A}}
\def\PRL{{\it Phys. Rev. Lett.}}
\def\RMS{{\it Russ. Math. Surv.}}
\titleaa{}{References}
\fono
\font\petit = cmr9
{\petit
For ease of the reader, we have collected here all the references quoted along the volume; we have
also added a substantial number of other works which were not quoted but which deal directly or are
concerned with, and/or relevant to, the general topic of Lie-point symmetries of differential
equations. This bibliography has no ambition to be complete (and we apologize to authors which were
not included only because of lack of attention by the present author), but we think it can be a
service to the reader and help him to know about the existence and location of a certain amount of
papers relevant to the topic; it seems to the author that this surely quite incomplete list is
nevertheless the biggest one available at this moment.
In the search for relevant papers, as the reader will easily notice, we have particularly
concentrated our attention on recent contribution; this list can be supplemented with the works
quoted in the bibliographic sections of Olver or Bluman and Kumei books. A number of older works are
also quoted, too; in particular we have tried to quote a number of very old issues concerned with
group analysis of differential equations we were aware of, to illustrate how the topic is not at all
new, and how substantial steps were performed a long time ago (which does not exclude that they could
have been forgotten for a while).
The reader will also immediately notice that we have not quoted the father of all the story, i.e.
Sophus Lie. The quotation of his complete works is, we think, implicit. Another, less easy to be
fixed, hole in the bibliography is constituted by russian works which were not translated into
western languages. Here no excuse is possible, and I can only apologize for not being able to acceed
the russian literature, first of all for not reading russian. Some list of russian references can be
find in the review papers (most of them appearing in {"Russian Mathematical Surveys"}) and books
written by russian authors and quoted here. }
\bigskip \bigskip
\parskip=5pt
\parindent=0pt
\def\space{\vskip 10pt}
{\tafont A}
Abers and Lee; "Gauge theories", {\it Phys. Rep.} {\bf 9} (1973), 1
R. Abraham and J.E. Marsden, "Foundations of mechanics", Benjamin, New York, 1978
B. Abraham-Shrauner, "Lie transformation group solutions of the nonlinear one-dimensional Vlasov
equation"; \JMP {\bf 26} (1985), 1428
B. Abraham-Shrauner, "Erratum : Lie transformation group solutions of the nonlinear
one-dimensional Vlasov equation [J. Math. Phys. 26, 1428 (1985)]" \JMP {\bf 26} (1985), 3204
B. Abraham-Shrauner and A. Guo, "Hidden symmetries associated with the projective group of nonlinear
first order ODEs"; \JPA {\bf 25} (1992), 5597
M. Abud and G. Sartori, "The geometry of spontaneous symmetry breaking"; {\it Ann. Phys.}
{\bf 150} (1983), 307
M. Aguirre, C. Friedli and J. Krause, "SL(3,R) as the group of symmetry transformation for all
one-dimensional linear systems. III. Equivalent Lagrangian formalism"; \JMP {\bf 33} (1992), 1571
M. Aguirre and J. Krause, "Infinitesimal symmetry transformations of some one-dimensional linear
systems"; \JMP {\bf 25} (1984), 210
M. Aguirre and J. Krause, "Infinitesimal symmetry transformations. II. Some one-dimensional
nonlinear systems"; \JMP {\bf 26} (1985), 593
M. Aguirre and J. Krause, "Some remarks on the Lie group of point transformations for the harmonic
oscillator"; \JPA {\bf 20} (1987) 3553
M. Aguirre and J. Krause, "SL(3,R) as the group of symmetry transformations for all
one-dimensional linear systems"; \JMP {\bf 29} (1988), 9
M. Aguirre and J. Krause, "SL(3,R) as the group of symmetry transformations for all
one-dimensional linear systems. II. Realizations of the Lie algebra"; \JMP {\bf 29} (1988), 1746
M. Aguirre and J. Krause, "Finite point transformation and linearization of ${\ddot x}=f(t,x)$";
\JPA {\bf 21} (1988), 2841
M. Aguirre and J. Krause, "General transformation theory of Lagrangian mechanics and the Lagrangian
group"; {\it Int. J. Theor. Phys.} {\bf 30} (1991), 495
M. Aguirre and J. Krause, "Point symmetry group of the Lagrangian"; {\it Int. J. Theor. Phys.}
{\bf 30} (1991), 1461
M.A. Almeida and I.C. Moreira: "Lie symmetries for the reduced three-wave interaction problem"; \JPA
{\bf 25} (1992), L669
A. Ambrosetti, V. Coti Zelati and I. Ekeland, "Symmetry breaking in hamiltonian
systems", {\it J. Diff. Eqs.} {\bf 67} (1987), 165
W.F. Ames, J.E. Peters and M. Abell, "Symmetry and semi-symmetry reduction in wave propagation and lubrication"; in Hussin ed. 1990
W.F. Ames and C. Rogers eds., "Nonlinear equations in applied sciences"; Academic Press, New York, 1992
R. Anderson, S. Kumei and C.E. Wulfman, "Generalisation of the concept of invariance of differential
equations". Results and applications to some Schroedinger equations"; \PRL {\bf 28}
(1972), 988
S. Antman, ed., "Applications of bifurcation theory", Academic Press, New York
(1977)
D. Armbruster and P. Chossat, "Heteroclinic orbits in a spherically invariant system"; {\it Physica D} {\bf 50} (1991), 155
V.I. Arnold, "Equations differentielles ordinaires", M.I.R., Moscow 1974; "Equations
Differentielles Ordinaires - IV edition", Mir, Moscow, 1990; "Ordinary Differential Equations - second edition", Springer Berlin, 1992
V.I. Arnold, "Les methodes mathematiques de la mecanique classique", M.I.R.,
Moscow 1976; "Mathematical Methods of Classical Mechanics"; Springer,
Berlin, 1978; II ed., 1989
V.I. Arnold, "Chapitres supplementaires de la thorie des equations
diffrentielles ordinaires", M.I.R., Moscow, 1980; "Geometrical Methods in
the Theory of Ordinary Differential Equations"; Springer, Berlin, 1983
V.I. Arnold, "Bifurcation and singularities in mathematics and mechanics"; in, "Theoretical and
applied mechanics, P. Germain et al. eds., North Holland 1989
V.I. Arnold; "Contact geometry and wave propagation"; Les Editions de L'Enseignement
Mathematique (Geneva), 1990
V.I. Arnold, S.M. Gusein-Zade and A.N. Varchenko, "Singularities of
differentiable mappings"; Birkhauser (Basel) 1985; "Singularites des applications
differentiables"; MIR, Moscow, 1986
V.I. Arnold and S.P. Novikov eds.; "Dynamical Systems IV", Encyclopaedia of
Mathematical Sciences, Springer (Berlin) 1990
E. Ascher and D. Gay, "Relative invariants of crystallographic point groups"; \JPA {\bf 18} (1985) 397
P.J. Aston, "Scaling laws and bifurcation"; in Roberts and Stewart 1991
P.J. Aston, "Analysis and computation of symmetry-breaking bifurcation and scaling laws using group
theoretic methods"; {\it SIAM J. Math. Anal.} {\bf 22} (1991) 181
P.J. Aston, "Local and global aspects of the $(1,n)$ mode interaction for capillary- gravity waves"; {\it Physica D} {\bf 52} (1991), 415
P.J. Aston, A. Spence and W. Wu, "Bifurcation to rotating waves in equations with O(2)-symmetry";
preprint 1991, to appear in {\it SIAM J. Math. Anal.}
C. Athorne, "On generalized Ermankov systems"; \PLA {\bf 159} (1991), 375
\space {\tafont B}
K. Babu Joseph and B.V. Baby, "Classical SU(2) Yang-Mills-Higgs system : Time-dependent solutions
by similarity method"; \JMP {\bf 26} (1985), 2746
V.A. Baikov, R.K. Gazizov and N.K. Ibragimov; {\it Math SSSR Sbornik} {\bf 64} (1989), 427
E. Barany, M. Golubitsky and J. Turski, "Bifurcations with local gauge symmetries in the Ginzburg- Landau equations"; {\it Physica D} {\bf 56} (1992), 36
A.O. Barut and A.J. Bracken, "Compact quantum systems: Internal geometry of relativistic systems";
\JMP {\bf 26}, 2515 (1985).
A.O. Barut, A. Inomata and R. Wilson, "A new realization of dynamical group and factorization
method"; \JPA {\bf 20} (1987), 4075
A.O. Barut, A. Inomata and R. Wilson, "Algebraic treatment of second Posch- Teller, Morse- Rosen and
Eckart equations"; \JPA {\bf 20} (1987), 4083
G. Baumann and M. Freyberger, "Generalised symmetries and conserved quantities of teh Lotka- Volterra model"; \PLA {\bf 156} (1991), 488
G. Baumann, M. Freyberger, W.G. Glockle and T.F. Nonnenmacher, "Symilarity solutions in
fragmentation kinetics"; \JPA {\bf 24} (1991), 5085
G. Baumann and T.F. Nonnenmacher, "Lie transformations, similarity reduction, and solutions for
the nonlinear Madelung fluid equations with external potential"; \JMP {\bf 28} (1987), 1250
J. Beckers and N. Debergh, "On the Lie extended method in quantum physics and its supersymmetric
version"; \JPA {\bf 23} (1990), L353
J. Beckers, N. Debergh and A.G. Nikitin, "More on the symmetries of the Schroedinger equation"; \JPA
{\bf 24} (1991), L1269
J. Beckers, D. Dehin and V. Hussin, "Symmetries and supersymmetries of the quantum harmonic
oscillator"; \JPA {\bf 20} (1987), 1137
J. Beckers, L. Gagnon, V. Hussin and P. Winternitz, "Superposition formulas for nonlinear
superequations"; \JMP {\bf 31} (1990), 2528
J. Beckers, V. Hussin, and P. Winternitz, "Nonlinear equations with superposition formulas and the
exceptional group $G(2)$. I. Complex and real forms of $g(2)$ and their maximal
subalgebras"; \JMP {\bf 27} (1986), 2217
J. Beckers, V. Hussin, and P. Winternitz, "Nonlinear equations with superposition formulas and the
exceptional group $ G(2)$. II. Classification of the equations"; \JMP {\bf 28}, 520 (1987)
L.M. Berkovic and M.L. Nechaevsky, "On the group properties and integrability
of the Fowler-Emden equations"; in M.A. Markov, V.I. Man'ko and A.E. Shabad 1985
J. Bertrand and G. Rideau, "Nonlinear representation of Poincar group in three dimensions"; \JMP
{\bf 28}, 1972 (1987)
E. Bierstone; {\it Topology} {\bf 14} (1975)
E. Bierstone, "The structure of orbit spaces
and the singularities of equivariant mappings", I.M.P.A., Rio de Janeiro (1980)
M. Biesiada and M. Szydlowski, "On some group properties of structure equations of stellar systems";
\JPA {\bf 21} (1988), 3409
G. Birkhoff, "Dimensional analysis of partial differential equations"; {\it Electr. Eng.} {\bf 67}
(1948), 1185
G. Birkhoff, "Hydrodynamics"; Princeton, 1960
G. Birkhoff and S. MacLane; "Elements of modern algebra", Macmillan (New York) 1941
G. Bluman, "Application of the general similarity solution of the heat equation to boundary-value
problems"; {\it Quart. Appl. Math.} {\bf 31} (1974), 403
G. Bluman, "A reduction algorithm for an ordinary differential equation admitting a solvable Lie
group"; {\it SIAM J. Appl. Math.} {\bf 50} (1990), 1689
G. Bluman, "Invariant solutions for ordinary differenial equations"; {\it SIAM J. Appl. Math.} {\bf 50} (1990), 1706
G. Bluman, "Potential symmetries"; in Hussin ed. 1990
G. Bluman, "Linearization of PDEs"; in Dodonov and Man'ko 1991 (p. 285)
G.W. Bluman and J.D. Cole, "The general similarity solution of the heat equation"; {\it J. Math.
Mech.} {\bf 18} (1969), 1025
G.W. Bluman and J.D. Cole, "Similarity methods for differential equations"; Springer
(New York) 1974
G. Bluman and S. Kumei, "On invariance properties of the wave equation"; \JMP {\bf 28} (1987), 307
G. Bluman and S. Kumei," Exact solutions for wave equations of two-layered media with
smooth transition"; \JMP {\bf 29}, 86 (1988)
G.W. Bluman and S. Kumei, "Symmetries and differential equations";
Springer, New York, 1989
G.W. Bluman, G.J. Reid, and S. Kumei, "New classes of symmetries for partial
differential equations"; \JMP {\bf 29} (1988), 806
G.W. Bluman, G.J. Reid, and S. Kumei, "Erratum : New classes of symmetries for partial
differential equations [J. Math. Phys. 29, 806 (1988)]"; \JMP {\bf 29}, 2320 (1988)
T.C. Bountis, V. Papageorgiou, and P. Winternitz, "On the integrability of systems of nonlinear
ordinary differential equations with superposition principles"; \JMP {\bf 27} (1986), 1215
C.P. Boyer and J.F. Plebanski, "An infinite hierarchy of conservation laws and nonlinear
superposition principles for self-dual Einstein spaces"; \JMP {\bf 26} (1985), 229
C.P. Boyer and P. Winternitz, "Symmetries of the self-dual Einstein equations. I. The
infinite-dimensional symmetry group and its low-dimensional subgroups"; \JMP {\bf 30} (1989), 1081
G.E. Bredon, "Introduction to Compact Transformation Groups", Academic Press,
New York, 1972
T.J. Bridges, "Hamiltonian bifurcation of the spatial structure for coupled nonlinear Schroedinger equations"; {\it Physica D} {\bf 57} (1992), 375
C.P. Bruter, ed., "Bifurcation theory, mechanics, and physics", Reidel,
Dordrecht, 1983
F.H. Busse, "Pattern of convection in spherical shells"; {\it J.
Fluid Mech.} {\bf 72} (1975), 65-85
F.H Busse and N. Riahi, "Pattern of convection in spherical shells, II"; {\it J. Fluid
Mech.} {\bf 123} (1982), 283-291
E. Buzano and M. Golubitsky, "Bifurcation on the hexagonal lattice and the plane
Benard problem"; {\it Phil. Trans. R. Soc. Lond.} {\bf A.308} (1983), 617-667
\vfill \eject
\space {\tafont C}
F. Cariello and M. Tabor, "Similarity reductions from extended Painlev\'e expansions for nonintegrable evolution equations"; {\it Physica D} {\bf 53} (1991), 59
J.F. Carinema, M.A. del Olmo and M. Santander, "A new look at dimensional analysis from a group
theoretical viewpoint"; \JPA {\bf 18} (1985), 1855
J.F. Carinena, M. A. Del Olmo, and M. Santander, "Locally operating realizations of transformation
Lie groups"; \JMP {\bf 26} (1985), 2096
J.F. Carinema, M.A. Del Olmo and P. Winternitz, "Cohomology and symmetry of
differential equations"; in Dodonov and Man'ko 1991 (p. 272)
J.F. Carinena, C. Lopez and E. Martinez, "A new approach to the converse of Noether's theorem"; \JPA
{\bf 22} (1989), 4777
J.F. Carinena and E. Martinez, "Symmetry theory and Lagrangian inverse problem for time-dependent
second order differential equations"; \JPA {\bf 22} (1989), 2659
J. Carr, "Applications of Centre Manifold Theory", Springer, New York, 1981
J.A. Cavalcante and K. Tenenblat, "Conservation laws for nonlinear evolution equations"; \JMP {\bf
29} (1988), 1044
G. Caviglia, "Composite variational principles and the determination of conservation laws"; \JMP
{\bf 29} (1988), 812
G. Caviglia and A. Morro, "Noether-type conservation laws for perfect fluid motions"; \JMP {\bf 28}
(1987), 1056
J.M. Cervero and J. Villarroel, "Contact symmetries and integrable non- linear dynamical systems";
\JPA {\bf 20} (1987), 6203
B. Champagne and P. Winternitz, "On the infinite-dimensional symmetry group of the Davey-Stewartson
equations"; \JMP {\bf 29} (1988), 1
B. Champagne, W. Hereman and P. Winternitz, "The computer calculation of Lie point
symmetries of large systems of differential equations"; {\it Comp. Phys. Comm.} {\bf 66} (1991), 319
D.R.J. Chillingworth, J.E. Marsden and Y.H. Wan, "Symmetry and bifurcation in the
three-dimensional elasticity"; {\it Arch. Rat. Mech. Anal.} {\bf 80} (1982), 295
D.R.J. Chillingworth, J.E. Marsden and Y.H. Wan, "Symmetry and bifurcation in the
three-dimensional elasticity II"; {\it Arch. Rat. Mech. Anal.} {\bf 83} (1982),
363
P. Chossat, "Bifurcation and stability of convective flows in rotating or not
rotating spherical shell"; {\it S.I.A.M. J. Appl. Math.} {\bf 37} (1979), 624
P. Chossat and M. Golubitsky, "Hopf bifurcation in the presence of symmetry,
center manifold and Liapunov-Schmidt reduction", in Atkinson et. al.
(1987), 343
P. Chossat and M. Golubitsky, "Iterates of maps with symmetry"; {\it SIAM J. Math. Anal.} {\bf 19}
(1988), 1259
S.N. Chow and J. Hale, "Methods of Bifurcation Theory", Springer, New York,
(1982)
G. Cicogna, "Symmetry breakdown from bifurcation"; {\it Lett. Nuovo Cimento} {\bf 31}
(1981), 600
G. Cicogna, "A nonlinear version of the equivariant bifurcation lemma"; \JPA {\bf 23} (1990),
L1339
G. Cicogna and G. Gaeta, "Periodic solutions from quaternionic bifurcation"; {\it Lett.
Nuovo Cimento} {\bf 44} (1985), 65
G. Cicogna and G. Gaeta, "Spontaneous linearization and periodic solutions in
Hopf and symmetric bifurcations"; {\it Phys. Lett. A} {\bf 116} (1986), 303
G. Cicogna and G. Gaeta, "Quaternionic bifurcation and SU(2) symmetry";
Preprint Pisa-IFU (1986)
G. Cicogna and G. Gaeta, "Hopf - type bifurcation in the presence of multiple
critical eigenvalues"; \JPA {\bf 20} (1987), L425
G. Cicogna and G. Gaeta, "Quaternionic-like bifurcation in the absence of
symmetry"; \JPA {\bf 20} (1987), 79
G. Cicogna and G. Gaeta, "Lie-point symmetries and Poincare' normal forms for
dynamical systems"; \JPA {\bf 23} (1990), L799
G. Cicogna and G. Gaeta, "Lie-point symmetries for autonomous systems and resonance";
\JPA {\bf 25} (1992), 1535
G. Cicogna and G. Gaeta, "Lie-point symmetries in bifurcation problems";
{\it Ann. Inst. H. Poincare'} {\bf 56} (1992), 375
G. Cicogna and G. Gaeta, "Lie-point symmetries in Mechanics"; {\it Nuovo Cimento}
{\bf B 107} (1992), 1085
G. Cicogna and G. Gaeta, "Nonlinear symmetries in bifurcation theory"; \PLA (1993)
G. Cicogna and D. Vitali, "Generalised symmetries of
Fokker-Planck - type equations"; {\it J. Phys. A} {\bf 22} (1989), L453
G. Cicogna and D. Vitali, "Classification of the extended symmetries of
Fokker-Planck equations"; {\it J. Phys. A} {\bf 23} (1990), L85
P.A. Clarkson, "New similarity solutions for the modified Boussinesq equation"; \JPA {\bf 22} (1989), 2355
P.A. Clarkson, "New similarity reduction and Painleve' analysis for the symmetric regularised long
wave and modified Benjamin-Bona-Mahoney equations"; \JPA {\bf 22} (1989), 3821
P.A. Clarkson, "Nonclassical symmetry reduction and exact solutions for physically significant nonlinear evolution equations"; in Rozmus and Tuszynski eds., 1991
P.A. Clarkson and S. Hood, "Symmetry reductions of a generalized, cylindrical Schroedinger
equation"; \JPA {\bf 26} (1993), 133
P.A. Clarkson and M.D. Kruskal, "New similarity reduction of the Boussinesq equation"; \JMP {\bf
30} (1989), 2201
P.A. Clarkson and J.A. Tuszynski, "Exact solutions of the multidimensional derivative nonlinear
Schroedinger equation for many-body systems near criticality"; \JPA {\bf 23} (1990), 4269
P.A. Clarkson and P. Winternitz, "Nonclassical symmetry reduction for the Kadomtsev- Petviashvili
equation"; {\it Physica D} {\bf 49} (1991), 257
E.A. Coddington and N. Levinson, "Theory of ordinary differential equations", Mc
Graw - Hill, London, 1955
S.V. Coggeshall and J. Meyer-ter-Vehn, "Group-invariant solutions and optiml systems for
multidimensional hydrodynamics"; \JMP {\bf 33} (1992), 3585
A. Cohen, "An introduction to the Lie theory of one-parameter groups with applications to the
solution of differential equations"; Boston 1911
J. Cole, "Scale factors and similarity solutions"; in Hussin ed. 1990
P. Collet and J.P. Eckmann, "Instabilities and fronts in extended systems", Princeton University
Press, 1990
R. Courant and D. Hilbert, "Methods of Mathematical Physics"; Wiley
M. Crandall and P. Rabinowitz, "Bifurcation from simple eigenvalues"; {\it J. Func.
Anal.} {\bf 8} (1971), 321
M. Crandall and P. Rabinowitz, "Bifurcation, perturbation of simple eigenvalues,
and linearized stability"; {\it Arch. Rat. Mech. Anal.} {\bf 52} (1973), 161
M. Crandall and P. Rabinowitz, "The Hopf bifurcation theorem in infinite
dimensions"; {\it Arch. Rat. Mech. Anal.} {\bf 67} (1977), 53
J.D. Crawford, "Surface waves in nonsquare containers with square symmetry"; {\it Phys. Rev. Lett.}
{\bf 67} (1991), 441
J.D. Crawford, "Introduction to Bifurcation Theory"; {\it Rev. Mod.
Phys.} (1991)
J.D. Crawford, "Normal forms for driven surface waves: boundary conditions, symmetry, and genericity"; {\it Physica D} {\bf 52} (1991), 429
J.D. Crawford, M. Golubitsky, M.G.M. Gomes, E. Knobloch and I. Stewart, "Boundary
conditions as symmetry constraints"; in "Singularity Theory and its Applications, Warwick 1989",
R.M. Roberts and I. Stewart eds., Lecture Notes in Mathematics, Springer, Berlin, 1991
J.D. Crawford and E. Knobloch, "Symmetry breaking bifurcations in O(2) maps";
\PLA {\bf 128}, 327
J.D. Crawford and E. Knobloch, "On degenerate Hopf
bifurcation with O(2) symmetry"; {\it Nonlinearity} {\bf 1} (1988), 617
J.D. Crawford and E. Knobloch, "Symmetry and symmetry-breaking bifurcations in fluid
dynamics"; {\it Ann. Rev. Fluid Mech.} {\bf 23} (1991), 341
\space {\tafont D}
E.N. Dancer, "On the existence of bifurcating solutions in the presence of
symmetries"; {\it Proc. Roy. Soc. Edin.} {\bf 85A} (1980), 321
E.N. Dancer, "An implicit function theorem with symmetries and its
application to nonlinear eigenvalues problems"; {\it Bull. Austral. Math.
Soc.} {\bf 21} (1980), 404
E.N. Dancer, "The G-invariant implicit function theorem in infinite
dimensions"; {\it Proc. Roy. Soc. Edin.} {\bf 92A} (1982), 13
E.N. Dancer, "Bifurcation under continuous groups of symmetry"; in
"Systems of Nonlinear Partial Differential Equations", J.M. Ball Ed.
Reidel, (1983), 343
E.N. Dancer, "The G-invariant implicit function theorem in infinite
dimensions Part II"; {\it Proc. Roy. Soc. Edin.} {\bf 102A} (1986), 211
Daniel and Viallet; "The geometrical setting of gauge theories of Yang-Mills type";
{\it Rev. Mod. Phys.} {\bf 52} (1980), 175
Y.A. Danilov and G.I. Kuznetsov, "Nonlinear equations and differential
invariants"; in M.A. Markov, V.I. Man'ko and A.E. Shabad 1985
G. Dattoli, M. Richetta, G. Schettini and A. Torre, "Lie algebraic methods and solutions of
linear partial differential equations"; \JMP {\bf 31} (1990), 2856
D. David, "Symmetry reduction for the KP equation and its Backlund
transformation"; in Gilmore 1987 (p. 451)
D. David, N. Kamran, D. Levi, and P. Winternitz, "Symmetry reduction for the Kadomtsev-Petviashvili
equation using a loop algebra"; \JMP {\bf 27} (1986), 1225
D. David, D. Levi and P. Winternitz, "Backlund transformations and the infinite-dimensional
symmetry group of the Kadomtsev- Petviashvili equation"; \PLA {\bf 118} (1986), 390
D. David, D. Levi and P. Winternitz, "Equations invariant under the symmetry group of the
Kadomtsev- Petviashvili equation"; \PLA {\bf 129} (1988), 161
G.F. Dell'Antonio and B.M. D'Onofrio, eds., "Recent advances in Hamiltonian systems"; World
Scientific, 1987
M.A. Del Olmo, M.A. Rodriguez and P. Winternitz, "Simple subgroups of simple Lie groups and
nonlinear differential equations with superposition principles"; \JMP {\bf 27} (1986), 14
M. Del Olmo, M.A. Rodriguez and P. Winternitz, "Superposition formulas for rectangular matrix
Riccati equations"; \JMP {\bf 28} (1987), 530
G. Denardo, G. Ghirardi and T. Weber, eds., "Group theoretical methods in Physics", proceedings of
the XII ICGTMP; {\it Lecture Notes in Physics} 201, Springer, Berlin, 1984
C. Deng- yuan, D. Levi and L. Yi- shen, "Equivalent classes of integrable non linear evolution
equations and generalised Miura transformation"; \JPA {\bf 20} (1987), 313
L.E. Dickson, "Differential equations from the group standpoint"; {\it Ann. Math.} {\bf 25} (1924),
287
R. Dirl and M. Moshinsky, "Accidental degeneracy and symmetry Lie algebra"; \JPA {\bf 18} (1985) 2423
J.M. Dixon, M. Kelley and J.A. Tuszynski, "Coherent structures from the three- dimensional nonlinear Schroedinger equation"; \PLA {\bf 170} (1992), 77
J.M. Dixon and J.A. Tuszynski, "Solutions of a generalized Emden equation and their physical
significance"; {\it Phys. Rev. A} {\bf 41} (1990), 4166
V.V. Dodonov and V.I. Man'ko, eds., "Group theoretical methods in physics"
(Proceedings of the XVIII ICGTMP, Moscow 1990), Lect. Notes Phys. 382, Springer,
Berlin, 1991
A. Doelman, "On the nonlinear evolution of patterns"; Ph.D. thesis, Utrecht, 1990
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\space {\tafont F}
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\space {\tafont G}
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