Algebraic operator method for the construction of solitary solutions to nonlinear differential equations
type: Item
instance of: scholarly article
title: Algebraic operator method for the construction of solitary solutions to nonlinear differential equations
zbMATH Open document ID: 1286.35223
author: Zenonas Navickas
author: Liepa Bikulciene
author: Maido Rahula
author: Minvydas Ragulskis
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2014-01-08T00:00:00Z
review text: Solutions of the KdV equation are derived by the algebraic operator method based on generalized operators of differentiation. This method is exploited for the derivation of analytic solutions to the KdV equation. The structure of solitary solutions and explicit conditions of existence of these solutions in the subspace of initial conditions are derived. It is shown that special solitary solutions exist only on a line in the parameter plane of initial and boundary conditions. This new theoretical result may lead to important findings in a variety of practical applications.
reviewed by: Masataka Kanki
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35C08
zbMATH DE Number: 6243530
zbMATH Keywords: KdV equation
zbMATH Keywords: general operator of differentiation
zbMATH Keywords: solitary solution
zbMATH Keywords: soliton solution
zbMATH Keywords: condition of existence
MaRDI profile type: Publication
full work available at URL: j.cnsns.2012.10.009
OpenAlex ID: W2066436194
DOI: 10.1016/J.CNSNS.2012.10.009
description: scientific article; zbMATH DE number 6243530