Exact Analytic Solutions Of Pochammer-Chree And Boussinesq Equations By Invariant Painleve Analysis And Generalized Hirota Techniques

Keywords

Exact solutions; Generalized infinite series; Hirota's method; Pochammer-Chree and Boussinesq equations; Truncated painleve expansions

Abstract

Combinations of truncated Painleve expansions, invariant Painleve analysis, and generalized Hirota series are used to solve ('partially reduce to quadrature') the integrable Boussinesq and the cubic and quintic generalized Pochammer-Chree (GPC) equation families. Although the multisolitons of the Boussinesq equation are very well-known, the solutions obtained here for all the three NLPDEs are novel, and non-trivial. All of the solutions obtained via invariant Painleve analysis are complicated rational functions, with arguments which themselves are trigonometric functions of various distinct traveling wave variables. This is reminiscent of doubly-periodic elliptic function solutions when nonlinear ODE systems are re- duced to quadratures. The solutions obtained using recently-generalized Hirota-type expansions are closer in functional form to conventional hyperbolic secant solutions, although with non-trivial traveling-wave arguments which are distinct for the two GPC equations.

Publication Date

1-1-2016

Publication Title

Discontinuity, Nonlinearity, and Complexity

Volume

5

Issue

2

Number of Pages

187-198

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.5890/DNC.2016.06.008

Socpus ID

85020283292 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85020283292

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