New variable separation excitations of (2+1)-dimensional dispersive long-water wave system obtained by an extended mapping approach

2005 ◽  
Vol 23 (5) ◽  
pp. 1741-1748 ◽  
Author(s):  
Chun-Long Zheng ◽  
Jian-Ping Fang ◽  
Li-Qun Chen
Keyword(s):  
Water Wave ◽  
Wave System ◽  
Variable Separation ◽  
Mapping Approach ◽  
Extended Mapping

Bell-Like and Peak-Like Loop Solitons in (2+1)-Dimensional Dispersive Long Water-Wave System

2006 ◽  
Vol 61 (1-2) ◽  
pp. 39-44
Author(s):  
Hai-Ping Zhu ◽  
Chun-Long Zheng ◽  
Jian-Ping Fang
Keyword(s):  
Water Wave ◽  
Wave System ◽  
Variable Separation ◽  
Mapping Approach ◽  
New Type ◽  
Extended Mapping ◽  
03.65 Ge

Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of the (2+1)-dimensional dispersive long water-wave (DLW) system is derived. Then based on the derived solution, we reveal some new types of loop solitons such as bell-like loop solitons and peak-like loop solitons in the (2+1)-dimensional DLW system. - PACS numbers: 05.45.Yv, 03.65.Ge

Localized Excitations in a Dispersive Long Water-Wave System via an Extended Projective Approach

2007 ◽  
Vol 62 (3-4) ◽  
pp. 140-146 ◽  
Author(s):  
Jin-Xi Fei ◽  
Chun-Long Zheng
Keyword(s):  
Coherent Structures ◽  
Water Wave ◽  
Wave System ◽  
Variable Separation ◽  
Localized Excitations ◽  
Complex Wave ◽  
New Type ◽  
03.65 Ge

By means of an extended projective approach, a new type of variable separation excitation with arbitrary functions of the (2+1)-dimensional dispersive long water-wave (DLW) system is derived. Based on the derived variable separation excitation, abundant localized coherent structures such as single-valued localized excitations, multiple-valued localized excitations and complex wave excitations are revealed by prescribing appropriate functions. - PACS numbers: 03.65.Ge, 05.45.Yv

Study of the Variable Separation Solutions and Chaotic Behaviors for the Extended (2+1)-Dimensional Shallow Water Wave System

2013 ◽  
Vol 329 ◽  
pp. 144-147
Author(s):  
Xiao Xin Zhu ◽  
Song Hua Ma ◽  
Qing Bao Ren
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Water Wave ◽  
Mapping Method ◽  
Separation Method ◽  
Wave System ◽  
Variable Separation ◽  
Wave Excitation ◽  
Shallow Water Wave ◽  
Variable Separation Method

With the mapping method and a variable separation method, a series of variable separation solutions to the extended (2+1)-dimensional shallow water wave (ESWW) system is derived. Based on the derived solitary wave excitation, some chaotic behaviors are investigated.

scholarly journals Time Evolution of Folded (2+1)-Dimensional Solitary Waves

2009 ◽  
Vol 64 (5-6) ◽  
pp. 309-314 ◽  
Author(s):  
Song-Hua Ma ◽  
Yi-Pin Lu ◽  
Jian-Ping Fang ◽  
Zhi-Jie Lv
Keyword(s):  
Solitary Wave ◽  
Elliptic Function ◽  
Water Wave ◽  
Periodic Wave ◽  
Wave System ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Variable Separation Approach

Abstract With an extended mapping approach and a linear variable separation approach, a series of solutions (including theWeierstrass elliptic function solutions, solitary wave solutions, periodic wave solutions and rational function solutions) of the (2+1)-dimensional modified dispersive water-wave system (MDWW) is derived. Based on the derived solutions and using some multi-valued functions, we find a few new folded solitary wave excitations.

scholarly journals Chaotic Solitons for the (2+1)-Dimensional Modified Dispersive Water-Wave System

2006 ◽  
Vol 61 (5-6) ◽  
pp. 249-252 ◽  
Author(s):  
Song-Hua Ma ◽  
Xiao-Hong Wu ◽  
Jian-Ping Fang ◽  
Chun-Long Zheng
Keyword(s):  
Solitary Wave ◽  
Water Wave ◽  
Wave System ◽  
Wave Excitation ◽  
Mapping Approach ◽  
03.65 Ge

With an improved mapping approach, a series of excitations of the (2+1)-dimensional modified dispersive water-wave (MDWW) system is derived. Based on the derived solitary wave excitation, we obtain some special chaotic solitons. - PACS numbers: 05.45.Yv, 03.65.Ge

Interaction Behaviours Among Special Solitons in the (2+1)-Dimensional Modified Dispersive Water-Wave System

2013 ◽  
Vol 68 (6-7) ◽  
pp. 447-453 ◽  
Author(s):  
Wen-Ting Zhang ◽  
Wei-Lu Chen ◽  
Li-Pu Zhang ◽  
Chao-Qing Dai
Keyword(s):  
Water Wave ◽  
Phase Shifts ◽  
Mapping Method ◽  
Wave System ◽  
Variable Separation

A modified mapping method is used to obtain variable separation solutions with two arbitrary functions of the (2+1)-dimensional modified dispersive water-wave system. Based on the variable separation solution and by selecting appropriate functions, we discuss interaction behaviours among special anti-solitons constructed by multi-valued functions. The analysis results exhibit that the interaction behaviours among special anti-dromion, dromion-like anti-peakon, and dromion-like anti-semifoldon are all non-completely elastic and phase shifts exist, while the interaction behaviour among dromionlike anti-semifoldons is completely elastic and without phase shifts.

New Mapping Solutions and Line Soliton Excitations in a (1+1)-Dimensional Dispersive Long-Water Wave System

2013 ◽  
Vol 432 ◽  
pp. 117-121
Author(s):  
Ying Shi ◽  
Bing Ke Wang ◽  
Song Hua Ma
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Water Wave ◽  
Solitary Wave Solution ◽  
Wave System ◽  
Variable Separation ◽  
New Family ◽  
Localized Excitations ◽  
Variable Separation Approach ◽  
Line Soliton

With the help of the symbolic computation system Maple and the mapping approach and a linear variable separation approach, a new family of exact solutions of the (1+1)-dimensional dispersive long-water wave system (DLWW) is derived. Based on the derived solitary wave solution, some novel localized excitations are investigated.

Solitons with Fusion and Fission Properties in the (2+1)-Dimensional Modified Dispersive Water-Wave System

2006 ◽  
Vol 61 (7-8) ◽  
pp. 307-315 ◽  
Author(s):  
Chao-Qing Dai ◽  
Rui-Pin Chen
Keyword(s):  
Riccati Equation ◽  
Water Wave ◽  
Equation Method ◽  
Wave System ◽  
Variable Separation ◽  
Projective Riccati Equation Method

In this paper, by means of the general projective Riccati equation method (PREM), the variable separation solutions of the (2+1)-dimensional modified dispersive water-wave system are obtained. By further studying, we find that these variable separation solutions, which seem independent, actually depend on each other. Based on the special variable separation solution and choosing suitable functions p and q, soliton fusion and fission phenomena among peakons, compactons, dromions and semifoldons are firstly investigated. - PACS numbers: 05.45.Yv, 02.30.Jr, 02.03Ik

New Variable Separation Excitations of a (2+1)-Dimensional Broer-Kaup-Kupershmidt System Obtained by an Extended Mapping Approach

2004 ◽  
Vol 59 (12) ◽  
pp. 912-918 ◽  
Author(s):  
Chun-Long Zheng ◽  
Jian-Ping Fang ◽  
Li-Qun Chen
Keyword(s):  
Variable Separation ◽  
Mapping Approach ◽  
New Type ◽  
Extended Mapping ◽  
03.65 Ge

Using an extended mapping approach, a new type of variable separation excitation with two arbitrary functions of the (2+1)-dimensional Broer-Kaup-Kupershmidt system (BKK) is derived. Based on this excitation, abundant propagating and non-propagating solitons, such as dromions, rings, peakons, compactons, etc. are found by selecting appropriate functions. - PACS: 05.45.Yv, 03.65.Ge

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