Perturbation of a singular solution to the Liouville equation
type: Item
instance of: scholarly article
title: Perturbation of a singular solution to the Liouville equation
zbMATH Open document ID: 0951.35082
DOI: 10.1007/BF02557326
published in: Theoretical and Mathematical Physics
publication date: 2000-12-14T00:00:00Z
review text: A formal asymptotic solution of the Cauchy problem \[ \partial^2_t u- \partial^2_xu+ 2e^u= \varepsilon F(u, \partial_x u,\partial_tu),\quad 0<\varepsilon\ll 1, \] \[ u|_{t= 0}= \psi_0(x; \varepsilon)\approx \sum^\infty_{n= 0} \varepsilon^n \psi_{0n}(x),\;\partial_t u|_{t=0}= \psi_1(x; \varepsilon)\approx \sum^\infty_{n= 0} \varepsilon^n \psi_{1n}(x) \] is constructed. It is assumed that the solution \[ \Phi(x, t)= \log 4{r_+'(x+ t)r_-'(x- t)\over [r+ (x+ t)+ r_-(x- t)]^2} \] of the unperturbed problem has singularities on the timelike lines (determined by the zeros of \(r_+(x+ t)+ r_-(x- t)\)).
reviewed by: Mihai Pascu
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 81Q15
zbMATH DE Number: 1465885
zbMATH Keywords: singularities on the timelike lines
author: L. A. Kalyakin
MaRDI profile type: Publication
cites work: Singular solutions of the equation (d'Alembert operator) \(\phi+(m^ 2/2)\exp \phi=0\) and dynamics of singularities
full work available at URL: https://doi.org/10.1007/bf02557326
OpenAlex ID: W2089158503
description: scientific article; zbMATH DE number 1465885