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

2003/11/25 by Sergej A. Choroszavin, Choroszavin, Sergej A. · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods for differential equations #Spectral Theory in Mathematical Physics #math-ph #math.DS #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0311045

Latex 2.09, subsection 3.3 reformed

openalex publication_date 2003/11/25 · arxiv created 2004/10/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 -4γ_acδ(x-x_a) Q_a(t) -4γ_bcδ(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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