03-509 Sergej A. Choroszavin ( sergius@pve.vsu.ru )
The Ground, a String, Two Elastic Springs. Simple Exactly Solvable Models of One-Dimensional Scalar Fields with Concentrated Factors. (50K, LaTeX 2.09) Nov 25, 03
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Abstract. This paper is an electronic application to my set of lectures, subject:`Formal methods in solving differential equations and constructing models of physical phenomena'. Addressed, mainly: postgraduates and related readers. Content: a discussion of the simple models ( I would rather say, toy models ) of the interaction based on equation arrays of the kind: d^2 u(t,x)/dt^2=c^{2}d^2 u(t,x)/dx^2 -4{\gamma_a}c\delta(x-x_a) Q_a(t) -4{\gamma_b}c\delta(x-x_b) Q_b(t), Q_a(t) = u(t,x_a), Q_b(t) = u(t,x_b). Central mathematical points: d'Alembert-Kirchhoff-like Formulae, Finite Rank Perturbations.

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