Nonlinear Green's functions for wave equation with quadratic and hyperbolic potentials
type: Item
instance of: scholarly article
title: Nonlinear Green's functions for wave equation with quadratic and hyperbolic potentials
zbMATH Open document ID: 1404.35297
DOI: 10.1155/2018/7179160
author: Asatur Zh. Khurshudyan
published in: Advances in Mathematical Physics
publication date: 2018-12-11T00:00:00Z
review text: Summary: The advantageous Green's function method that originally has been developed for nonhomogeneous linear equations has been recently extended to nonlinear equations by Frasca. This article is devoted to rigorous and numerical analysis of some second-order differential equations new nonlinearities by means of Frasca's method. More specifically, we consider one-dimensional wave equation with quadratic and hyperbolic nonlinearities. The case of exponential nonlinearity has been reported earlier. Using the method of generalized separation of variables, it is shown that a hierarchy of nonlinear wave equations can be reduced to second-order nonlinear ordinary differential equations, to which Frasca's method is applicable. Numerical error analysis in both cases of nonlinearity is carried out for various source functions supporting the advantage of the method.
Mathematics Subject Classification ID: 35L71
Mathematics Subject Classification ID: 35A08
zbMATH DE Number: 6992006
zbMATH Keywords: Frasca's method
zbMATH Keywords: generalized separation of variables
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/7179160
OpenAlex ID: W2806560364
cites work: Solving frontier problems of physics: the decomposition method
cites work: Q4828547
cites work: The \((\frac{G'}{G})\)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
cites work: Green's functions with applications
cites work: Duals and propagators: A canonical formalism for nonlinear equations
cites work: Propagators for non-linear systems
cites work: Benchmarking the propagator method for nonlinear systems: a Burgers-Korteweg-deVries equation
cites work: GREEN FUNCTION METHOD FOR NONLINEAR SYSTEMS
cites work: GREEN FUNCTIONS AND NONLINEAR SYSTEMS: SHORT TIME EXPANSION
cites work: Existence of positive solutions for two-point boundary value problems of nonlinear finite discrete fractional differential equations and its application
cites work: Hyers-Ulam stability and existence of solutions for Nigmatullin's fractional diffusion equation
cites work: Green’s function approach in approximate controllability for nonlinear physical processes
cites work: Generalized separation of variables and exact solutions of nonlinear equations
Wikidata QID: Q129729956
description: scientific article; zbMATH DE number 6992006