- 02-486 A A Alexeyev
- A multidimensional superposition principle: classical solitons II
Nov 25, 02
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Abstract. A concept introduced previously as an approach for finding superposition formulas of nonlinear PDEs and explanation of various types wave interactions in such systems is developed further, both from the theoretical and technical point of view. In its framework, in the framework of the multidimensional superposition principle, a straightforward and self-consistent technique for constructing the related invariant manifolds in soliton cases is proposed.
The method is illustrated by simple examples, which, in particular, show principle generality between conventional linear PDEs and soliton nonlinear equations. The demonstration that so-called truncated singular expansions can be associated with some sort of the above soliton invariant manifolds is presented as well.