Solutions of the Boussinesq equation
type: Item
instance of: scholarly article
title: Solutions of the Boussinesq equation
zbMATH Open document ID: 0613.35068
DOI: 10.1016/0167-2789(86)90088-6
published in: Physica D
publication date: 1986-01-01T00:00:00Z
review text: The rational solutions of the Boussinesq equation (mainly those which decay to zero when x goes to infinity) are studied. The solution is written in terms of a function which is assumed to have a polynomial form, and the coefficients are computed. It is interesting to emphasize that rational solutions exist only for some value of maximal degree of the polynomials. Finally, the solutions are computed using the Bäcklund transformations.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 3992052
zbMATH Keywords: rational solutions
zbMATH Keywords: Boussinesq equation
zbMATH Keywords: Bäcklund transformations
author: Hélène Airault
reviewed by: Gelu Paşa
MaRDI profile type: Publication
full work available at URL: 0167-2789(86)90088-6
OpenAlex ID: W2055787806
cites work: Rational and elliptic solutions of the korteweg-de vries equation and a related many-body problem
cites work: Boussinesq's equation on the circle
cites work: Solitons and rational solutions of nonlinear evolution equations
cites work: Q4151763
cites work: Meromorphic solutions of nonlinear partial differential equations and many-particle completely integrable systems
cites work: The Painlevé property and Bäcklund transformations for the sequence of Boussinesq equations
cites work: Infinite dimensional Lie algebras. An introduction
cites work: Operator Approach to the Kadomtsev-Petviashvili Equation–Transformation Groups for Soliton Equations III–
cites work: Loop groups and equations of KdV type
cites work: On a class of polynomials connected with the Korteweg-de Vries equation
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description: scientific article; zbMATH DE number 3992052