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

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

New Exact Solutions and Fractal Localized Structures for the (2+1)-Dimensional Boiti-Leon-Pempinelli System

2005 ◽  
Vol 60 (4) ◽  
pp. 245-251 ◽  
Author(s):  
Jian-Ping Fang ◽  
Qing-Bao Ren ◽  
Chun-Long Zheng
Keyword(s):  
Solitary Wave ◽  
Coherent Structures ◽  
Variable Separation ◽  
Wave Excitation ◽  
Interesting Phenomenon ◽  
New Exact Solutions ◽  
Localized Structures ◽  
Fractal Properties ◽  
New Type ◽  
03.65 Ge

Abstract In this work, a novel phenomenon that localized coherent structures of a (2+1)-dimensional physical model possess fractal properties is discussed. To clarify this interesting phenomenon, we take the (2+1)-dimensional Boiti-Leon-Pempinelli (BLP) system as a concrete example. First, with the help of an extended mapping approach, a new type of variable separation solution with two arbitrary functions is derived. Based on the derived solitary wave excitation, we reveal some special regular fractal and stochastic fractal solitons in the (2+1)-dimensional BLP system. - PACS: 05.45.Yv, 03.65.Ge

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.

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

Folded Solitary Waves and Foldons in the (2+1)-Dimensional Long Dispersive Wave Equation

2003 ◽  
Vol 58 (5-6) ◽  
pp. 280-284
Author(s):  
J.-F. Zhang ◽  
Z.-M. Lu ◽  
Y.-L. Liu
Keyword(s):  
Wave Equation ◽  
Solitary Waves ◽  
Coherent Structures ◽  
Bäcklund Transformation ◽  
Dispersive Wave ◽  
Variable Separation ◽  
New Class ◽  
Localized Structures ◽  
Dispersive Wave Equation ◽  
03.65 Ge

By means of the Bäcklund transformation, a quite general variable separation solution of the (2+1)- dimensional long dispersive wave equation: λqt + qxx − 2q ∫ (qr)xdy = 0, λrt − rxx + 2r ∫ (qr)xdy= 0, is derived. In addition to some types of the usual localized structures such as dromion, lumps, ring soliton and oscillated dromion, breathers soliton, fractal-dromion, peakon, compacton, fractal and chaotic soliton structures can be constructed by selecting the arbitrary single valued functions appropriately, a new class of localized coherent structures, that is the folded solitary waves and foldons, in this system are found by selecting appropriate multi-valuded functions. These structures exhibit interesting novel features not found in one-dimensions. - PACS: 03.40.Kf., 02.30.Jr, 03.65.Ge.

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.

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.

New Exact Solutions and Localized Excitations in a (2+1)-Dimensional Soliton System

2009 ◽  
Vol 64 (1-2) ◽  
pp. 37-43
Author(s):  
Song-Hua Ma ◽  
Jian-Ping Fang
Keyword(s):  
Exact Solutions ◽  
Water Wave ◽  
Reduction Method ◽  
Wave System ◽  
Similarity Reduction ◽  
New Exact Solutions ◽  
Localized Excitations ◽  
Reduction Equation ◽  
Dimensional Soliton

Starting from a special conditional similarity reduction method, we obtain the reduction equation of the (2+1)-dimensional dispersive long-water wave system. Based on the reduction equation, some new exact solutions and abundant localized excitations are obtained.

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