An integral representation of solutions to the Klein-Gordon equation
type: Item
instance of: scholarly article
title: An integral representation of solutions to the Klein-Gordon equation
zbMATH Open document ID: 0941.35081
author: A. M. Khapaev
author: A. A. Tsygankov
published in: Computational Mathematics and Mathematical Physics
publication date: 2000-04-05T00:00:00Z
review text: The authors analyze the method for constructing the analytical solution to the Klein-Gordon equation in the case of a plane-wave electromagnetic field. The problem under study has been reduced to the Cauchy problem for a parabolic equation. The solutions have been constructed in the form of series in the Hermite and Laguerre polynomials, which makes it difficult to calculate quantum-mechanical processes, especially when the field is the superposition of a stationary magnetic field and a plane-wave field. This motivates the construction of solutions to the Cauchy problem in integral form, performed in the present paper.
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 35C15
zbMATH DE Number: 1427855
zbMATH Keywords: analytical solution to the Klein-Gordon equation
zbMATH Keywords: Cauchy problem for a parabolic equation
reviewed by: A. Tret'yakov
MaRDI profile type: Publication
Recommended article: Integrability of Klein–Gordon Equations
Recommended article: Exact, approximate and asymptotic solutions of the Klein-Gordon integral equation
Recommended article: An integral equation formalism for solving the nonlinear Klein-Gordon equation
Recommended article: On the solutions of Klein-Gordon equation
Recommended article: Solutions of the perturbed Klein-Gordon equations
Recommended article: Q3538387
Recommended article: Integral representation of the solution of a Gellerstedt problem
Recommended article: Q4809862
Recommended article: Q4657927
Recommended article: Q3283117
description: scientific article; zbMATH DE number 1427855