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The Ground, a String, Two Elastic Springs. Simple Exactly Solvable Models of One-Dimensional Scalar Fields with Concentrated Factors

Sergej A. Choroszavin
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Abstract

This paper is a basis of a part of 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{γ_a}cδ(x-x_a) Q_a(t) -4{γ_b}cδ(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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Sergej A. Choroszavin. 2004-10-20. The Ground, a String, Two Elastic Springs. Simple Exactly Solvable Models of One-Dimensional Scalar Fields with Concentrated Factors. https://arxiv.org/abs/math-ph/0311045

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