Painleve Analysis and Symmetries of the Hirota­Satsuma Equation

DOI

10.2991/jnmp.1996.3.1-2.17How to use a DOI?

Abstract

The singular manifold expansion of Weiss, Tabor and Carnevale [1] has been successfully applied to integrable ordinary and partial differential equations. They yield information such as Lax pairs, Bäcklund transformations, symmetries, recursion operators, pole dynamics, and special solutions. On the other hand, several recent developments have made the application of group theory to the solution of the differential equations more powerful then ever. More recently, Gibbon et. al. [2] revealed interrelations between the Painlevè property and Hirota's bilinear method. And W. Strampp [3] hase shown that symmetries and recursion operators for an integrable nonlinear partial differential equation can be obtained from the Painlevè expansion. In this paper, it has been shown that the Hirota­Satsuma equation passes the Painlevé test given by Weiss et al. for nonlinear partial differential equations. Furthermore, the data obtained by the truncation technique is used to obtain the symmetries, recursion operators, some analytical solutions of the Hirota­Satsuma equation.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - A.A. Mohammad
AU  - M. Can
PY  - 1996
DA  - 1996/05/01
TI  - Painleve Analysis and Symmetries of the Hirota­Satsuma Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 152
EP  - 155
VL  - 3
IS  - 1-2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1996.3.1-2.17
DO  - 10.2991/jnmp.1996.3.1-2.17
ID  - Mohammad1996
ER  -