An Interaction of An Oscillator with An One-Dimensional Scalar Field. Simple Exactly Solvable Models based on Finite Rank Perturbations Methods. I: D'Alembert-Kirchhoff-like formulae

الأصل · EN

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 very detailed discussion of the simple model of interaction based on the equation array: d² q(t)/dt² =-Ω²(q(t)-Q(t))+f₀(t), d²u(t,x)/t²=c²d² u(t,x)/dx ² -4γcδ(x-x₀)(Q(t)-q(t)) +f₁(t,x), Q(t) = u(t,x₀). Besides, less detailed discussion of related models. Central mathematical points: d'Alembert-Kirchhoff-like formulae. Central physical points: phenomena of Radiation Reaction, Braking Radiation and Resonance.