Residual symmetry, Bäcklund transformation and CRE solvability of a ( $$\mathbf{2}{\varvec{+}}{}... Nonlinear Dyn https://doi.org/10.1007/s11071-018-4371-2 ORIGINAL PAPER Residual symmetry, Bäcklund transformation and CRE solvability of a (2+1)-dimensional nonlinear system Zhonglong Zhao · Bo Han Received: 19 January 2018 / Accepted: 15 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract In this paper, the truncated Painlevé expan- Keywords (2 + 1)-dimensional sine-Gordon equa- sion is employed to derive a Bäcklund transformation tion · Residual symmetry · Bäcklund transformation · of a (2 + 1)-dimensional nonlinear system. This sys- CRE solvability · Lump-type solutions · Soliton– tem can be considered as a generalization of the sine- cnoidal wave solutions Gordon equation to 2 + 1 dimensions. The residual symmetry is presented, which can be localized to the 1 Introduction Lie point symmetry by introducing a prolonged system. The multiple residual symmetries and the nth Bäcklund Mathematical models play a signiﬁcant part while deal- transformation in terms of determinant are obtained. ing with science and engineering problems [1–4]. As Based on the Bäcklund transformation from the trun- one of the main parts of the mathematical models, the cated Painlevé expansion, lump and lump-type solu- partial differential equations (PDEs) have been widely tions of this system are constructed. Lump wave http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Dynamics Springer Journals # Residual symmetry, Bäcklund transformation and CRE solvability of a ($$\mathbf{2}{\varvec{+}}{} \mathbf{1} 2 + 1 )-dimensional nonlinear system

, Volume OnlineFirst – May 30, 2018
14 pages

/lp/springer_journal/residual-symmetry-b-cklund-transformation-and-cre-solvability-of-a-IAe6FhTYfN
Publisher
Springer Netherlands
Subject
Engineering; Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering
ISSN
0924-090X
eISSN
1573-269X
D.O.I.
10.1007/s11071-018-4371-2
Publisher site
See Article on Publisher Site

### Abstract

Nonlinear Dyn https://doi.org/10.1007/s11071-018-4371-2 ORIGINAL PAPER Residual symmetry, Bäcklund transformation and CRE solvability of a (2+1)-dimensional nonlinear system Zhonglong Zhao · Bo Han Received: 19 January 2018 / Accepted: 15 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract In this paper, the truncated Painlevé expan- Keywords (2 + 1)-dimensional sine-Gordon equa- sion is employed to derive a Bäcklund transformation tion · Residual symmetry · Bäcklund transformation · of a (2 + 1)-dimensional nonlinear system. This sys- CRE solvability · Lump-type solutions · Soliton– tem can be considered as a generalization of the sine- cnoidal wave solutions Gordon equation to 2 + 1 dimensions. The residual symmetry is presented, which can be localized to the 1 Introduction Lie point symmetry by introducing a prolonged system. The multiple residual symmetries and the nth Bäcklund Mathematical models play a signiﬁcant part while deal- transformation in terms of determinant are obtained. ing with science and engineering problems [1–4]. As Based on the Bäcklund transformation from the trun- one of the main parts of the mathematical models, the cated Painlevé expansion, lump and lump-type solu- partial differential equations (PDEs) have been widely tions of this system are constructed. Lump wave

### Journal

Nonlinear DynamicsSpringer Journals

Published: May 30, 2018

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