New Types of Solitons with Fusion and Fission Properties in the (2+1)-Dimensional Generalized Broer-Kaup System

2006 ◽  
Vol 61 (10-11) ◽  
pp. 519-524
Author(s):  
Chao-Qing Dai ◽  
Jun-Lang Chen
Keyword(s):  
Arbitrary Number ◽  
Bäcklund Transformation ◽  
Variable Separation ◽  
Backlund Transformation ◽  
Linear Superposition ◽  
Soliton Fission ◽  
Superposition Theorem

In this paper, by virtue of a special Painlevé-Bäcklund transformation and the linear superposition theorem, the general variable separation solution with an arbitrary number of variable separated functions of the generalized Broer-Kaup (GBK) system is obtained. Based on the general variable separation solution with some suitable variable separated functions, new types of the V-shaped soliton fusion and Y-shaped soliton fission are firstly investigated. - PACS numbers: 05.45.Yv, 02.30.Jr, 02.03Ik

scholarly journals Solitary wave fission and fusion in the (2+1)-dimensional generalized Broer–Kaup system

2012 ◽  
Vol 17 (3) ◽  
pp. 271-279 ◽  
Author(s):  
Chaoqing Dai ◽  
Cuiyun Liu
Keyword(s):  
Solitary Wave ◽  
Bäcklund Transformation ◽  
Variable Separation ◽  
Backlund Transformation ◽  
Linear Superposition ◽  
Superposition Theorem

Via a special Painlevé–Bäcklund transformation and the linear superposition theorem, we derive the general variable separation solution of the (2 + 1)-dimensional generalized Broer–Kaup system. Based on the general variable separation solution and choosing some suitable variable separated functions, new types of V-shaped and A-shaped solitary wave fusion and Y-shaped solitary wave fission phenomena are reported.

Exact Solutions and Localized Excitations of Burgers System in (3+1) Dimensions

2011 ◽  
Vol 66 (6-7) ◽  
pp. 383-391 ◽  
Author(s):  
Chun-Long Zheng ◽  
Hai-Ping Zhu
Keyword(s):  
Linear System ◽  
Exact Solutions ◽  
The Novel ◽  
Variable Separation ◽  
Linear Superposition ◽  
Localized Excitations ◽  
New Type ◽  
Superposition Theorem ◽  
Burgers System

With the help of a Cole-Hopf transformation, the nonlinear Burgers system in (3+1) dimensions is reduced to a linear system. Then by means of the linear superposition theorem, a general variable separation solution to the Burgers system is obtained. Finally, based on the derived solution, a new type of localized structure, i.e., a solitonic bubble is revealed and some evolutional properties of the novel localized structure are briefly discussed

scholarly journals Nonlocal Symmetry and Bäcklund Transformation of a Negative-Order Korteweg–de Vries Equation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Jinxi Fei ◽  
Weiping Cao ◽  
Zhengyi Ma
Keyword(s):  
Vries Equation ◽  
Bäcklund Transformation ◽  
Backlund Transformation ◽  
Nonlocal Symmetry ◽  
Linear Superposition ◽  
Residual Symmetry ◽  
Negative Order ◽  
De Vries ◽  
Finite Transformation ◽  
New Variables

The residual symmetry of a negative-order Korteweg–de Vries (nKdV) equation is derived through its Lax pair. Such residual symmetry can be localized, and the original nKdV equation is extended into an enlarged system by introducing four new variables. By using Lie’s first theorem, we obtain the finite transformation for the localized residual symmetry. Furthermore, we localize the linear superposition of multiple residual symmetries and construct n-th Bäcklund transformation for this nKdV equation in the form of the determinants.

Nonlocal symmetries, Bäcklund transformation and interaction solutions for the integrable Boussinesq equation

2020 ◽  
Vol 34 (26) ◽  
pp. 2050288
Author(s):  
Jun Cai Pu ◽  
Yong Chen
Keyword(s):  
Boussinesq Equation ◽  
Bäcklund Transformation ◽  
Superposition Principle ◽  
Symmetry Transformation ◽  
Backlund Transformation ◽  
Nonlocal Symmetry ◽  
Linear Superposition ◽  
Nonlocal Symmetries ◽  
Interaction Solutions ◽  
Physical Phenomena

The nonlocal symmetry of the integrable Boussinesq equation is derived by the truncated Painlevé method. The nonlocal symmetry is localized to the Lie point symmetry by introducing auxiliary-dependent variables and the finite symmetry transformation related to the nonlocal symmetry is presented. The multiple nonlocal symmetries are obtained and localized base on the linear superposition principle, then the determinant representation of the [Formula: see text]th Bäcklund transformation is provided. The integrable Boussinesq equation is also proved to be consistent tanh expansion (CTE) form and accurate interaction solutions among solitons and other types of nonlinear waves are given out analytically and graphically by the CTE method. The associated structure may be related to large variety of real physical phenomena.

EXACT SOLUTIONS AND COMPLEX WAVE EXCITATIONS OF GENERALIZED SASA–SATSUMA SYSTEM IN (2+1)-DIMENSIONS

2009 ◽  
Vol 23 (19) ◽  
pp. 3931-3938 ◽  
Author(s):  
CHUN-LONG ZHENG ◽  
JIAN-FENG YE
Keyword(s):  
Exact Solutions ◽  
Solitary Waves ◽  
Bäcklund Transformation ◽  
Periodic Wave ◽  
Variable Separation ◽  
Backlund Transformation ◽  
Complex Wave

Starting from a Painlevé–Bäcklund transformation, an exact variable separation solution with four arbitrary functions for the (2+1)-dimensional generalized Sasa–Satsuma (GSS) system are derived. Based on the derived exact solutions in the paper, some complex wave excitations in the (2+1)-dimensional GSS system and revealed, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave background are also briefly discussed.

scholarly journals Residual Symmetries and Bäcklund Transformations of (2 + 1)-Dimensional Strongly Coupled Burgers System

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Haifeng Wang ◽  
Yufeng Zhang
Keyword(s):  
General Theory ◽  
Bäcklund Transformation ◽  
Symmetry Analysis ◽  
Point Symmetry ◽  
Backlund Transformation ◽  
Linear Superposition ◽  
Strongly Coupled ◽  
Residual Symmetry ◽  
Commutative Subalgebra ◽  
Burgers System

In this article, we mainly apply the nonlocal residual symmetry analysis to a (2 + 1)-dimensional strongly coupled Burgers system, which is defined by us through taking values in a commutative subalgebra. On the basis of the general theory of Painlevé analysis, we get a residual symmetry of the strongly coupled Burgers system. Then, we introduce a suitable enlarged system to localize the nonlocal residual symmetry. In addition, a Bäcklund transformation is derived by Lie’s first theorem. Further, the linear superposition of the multiple residual symmetries is localized to a Lie point symmetry, and an N-th Bäcklund transformation is also obtained.

Localized Coherent Soliton Structures in a Generalized (2+1)-Dimensional Nonlinear Schrödinger System

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4407-4414 ◽  
Author(s):  
Chun-Long Zheng ◽  
Zheng-Mao Sheng
Keyword(s):  
Coherent Structures ◽  
Bäcklund Transformation ◽  
Variable Separation ◽  
Backlund Transformation ◽  
Nonlinear Schrödinger ◽  
Localized Structures ◽  
Nonlinear Schrödinger System ◽  
Localized Excitations ◽  
Schrödinger System ◽  
Variable Separation Approach

A variable separation approach is used to obtain localized coherent structures in a generalized (2+1)-dimensional nonlinear Schrödinger system. Applying a special Bäcklund transformation and introducing arbitrary functions of the seed solutions, the abundance of the localized structures of this system are derived. By selecting the arbitrary functions appropriately, some special types of localized excitations such as dromions, dromion lattice, peakons, breathers and instantons are constructed.

GENERAL VARIABLE SEPARATION SOLUTION AND EXOTIC LOCALIZED STRUCTURES OF NEW (2+1)-DIMENSIONAL SOLITON EQUATION

2005 ◽  
Vol 19 (12) ◽  
pp. 2011-2044 ◽  
Author(s):  
CHENG-LIN BAI ◽  
CHENG-JIE BAI ◽  
HONG ZHAO
Keyword(s):  
Bäcklund Transformation ◽  
Variable Separation ◽  
Backlund Transformation ◽  
Soliton Equation ◽  
Localized Structures ◽  
New Novel ◽  
Localized Excitations ◽  
Dimensional Soliton

By applying a special Bäcklund transformation, a quite general variable separation solution for new (2+1)-dimensional soliton equation is derived. In addition to some types of the usual localized excitations such as dromion, lumps, ring soliton, oscillated dromion and breathers soliton structures can be easily constructed by selecting the arbitrary functions appropriately, a new novel class of localized structures like fractal-dromion, fractal-lump, peakon, compacton and folded excitation of this system are found by selecting appropriate functions. Some interesting novel features of these structures are revealed.

New Multi-Soliton Solutions of the (2+1)-Dimensional Breaking Soliton Equations

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4376-4381 ◽  
Author(s):  
Jie-Fang Zhang ◽  
Chun-Long Heng
Keyword(s):  
Bäcklund Transformation ◽  
Direct Method ◽  
Soliton Solutions ◽  
Variable Separation ◽  
Backlund Transformation ◽  
Soliton Equations ◽  
Simplified Form

A simple and direct method is used to solve the (2+1)-dimensional breaking soliton equations: qt=iqxy-2iq∫(qr)ydx, rt=-irxy+2ir∫(qr)ydx. This technique yields a simplified form of the (2+1)-dimensional breaking soliton equations by use of a special Bäcklund transformation and a variable separation solution of this model is derived. Some special types of multi-soliton structure are constructed by selecting the arbitrary functions and arbitrary constants appropriately.

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