The Ground, a String, Two Elastic Springs. Simple Exactly Solvable Models of One-Dimensional Scalar Fields with Concentrated Factors
Sergej A. Choroszavin
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: d2 u(t,x)/dt2=c2d2 u(t,x)/dx2 -4γacδ(x-xa) Qa(t) -4γbcδ(x-xb) Qb(t), Qa(t) = u(t,xa), Qb(t) = u(t,xb). Central mathematical points: d'Alembert-Kirchhoff-like Formulae, Finite Rank Perturbations.
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