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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus

12 Issues per year


IMPACT FACTOR 2016: 1.432

CiteScore 2017: 1.30

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1865-7109
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Volume 72, Issue 9

Issues

The Residual Symmetry and Consistent Tanh Expansion for the Benney System

Zheng-Yi Ma
  • Corresponding author
  • Department of Mathematics, Lishui University, Lishui 323000, P.R. China
  • Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, P.R. China
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/ Jin-Xi Fei / Jun-Chao Chen
Published Online: 2017-08-07 | DOI: https://doi.org/10.1515/zna-2017-0191

Abstract

The residual symmetry of the (2+1)-dimensional Benney system is derived from the truncated Painlevé expansion. Such residual symmetry is localised and the original Benney equation is extended into an enlarged system by introducing four new variables. By using Lies first theorem, we obtain the finite transformation for the localised residual symmetry. More importantly, we further localise the linear superposition of multiple residual symmetries and construct the nth Bäcklund transformation for the Benney system in the form of the determinant. Moreover, it is proved that the (2+1)-dimensional Benney system is consistent tanh expansion (CTE) solvable. The exact interaction solutions between solitons and any other types of potential Burgers waves are also obtained, which include soliton-error function waves, soliton-periodic waves, and so on.

Keywords: Benney System; CTE Solvability; nth Bäcklund Transformation, Exact Interaction Solution; Residual Symmetry

PACS: 02.30.Jr; 02.20.-a; 04.20.Jb; 05.45.Yv

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About the article

Received: 2017-06-03

Accepted: 2017-07-11

Published Online: 2017-08-07

Published in Print: 2017-08-28


Citation Information: Zeitschrift für Naturforschung A, Volume 72, Issue 9, Pages 863–871, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-2017-0191.

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