Application of the Improved Mapping Approach to Exact Solutions and Chaotic Patterns for a Nonlinear Equation

2014 ◽  
Vol 945-949 ◽  
pp. 2430-2434
Author(s):  
Yan Lei ◽  
Song Hua Ma ◽  
Jian Ping Fang
Keyword(s):  
Nonlinear Equation ◽  
Exact Solutions ◽  
Variable Separation ◽  
Mapping Approach ◽  
Localized Excitations ◽  
Variable Separation Approach

Starting from an improved mapping approach and a linear variable separation approach, a series of exact solutions of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli system (BLMP) is derived. Based on the derived variable separated solution, we obtain some special localized excitations such as dromion, solitoff and chaotic patterns.

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

Multi-Soliton Excitations and Chaotic Patterns for the (2+1)-Dimensional Breaking-Soliton System

2010 ◽  
Vol 65 (6-7) ◽  
pp. 477-482 ◽  
Author(s):  
Li-Chen Lü ◽  
Song-Hua Ma ◽  
Jian-Ping Fang
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Wave Solutions ◽  
Localized Excitations ◽  
Variable Separation Approach

Starting from a projective equation and a linear variable separation approach, some solitary wave solutions with arbitrary functions for the (2+1)-dimensional breaking soliton system are derived. Based on the derived solution and by selecting appropriate functions, some novel localized excitations such as multi-solitons and chaotic-solitons are investigated.

Exact Solutions and Solitons with Fission and Fusion Properties for the Generalized Broer-Kaup System

2006 ◽  
Vol 61 (1-2) ◽  
pp. 16-22
Author(s):  
Chun-Long Zheng ◽  
Jian-Ping Fang
Keyword(s):  
Exact Solutions ◽  
Variable Separation ◽  
Soliton Fission ◽  
Dimensional Soliton ◽  
Variable Separation Approach ◽  
03.65 Ge

Starting from a Painlev´e-B¨acklund transformation and a linear variable separation approach, we obtain a quite general variable separation excitation to the generalized (2+1)-dimensional Broer-Kaup (GBK) system. Then based on the derived solution, we reveal soliton fission and fusion phenomena in the (2+1)-dimensional soliton system. - PACS numbers: 05.45.Yv, 03.65.Ge

Variable Separation Approach for the Sine-Gordon System

2004 ◽  
Vol 59 (10) ◽  
pp. 629-634 ◽  
Author(s):  
Xian-jing Lai ◽  
Jie-fang Zhang
Keyword(s):  
Solitary Waves ◽  
Periodic Waves ◽  
Variable Separation ◽  
Elastic Interactions ◽  
Localized Excitations ◽  
Variable Separation Approach

Using the B¨acklund transformation and a variable separation approach with some arbitrary functions, three new types of solutions of the sine-Gordon system have been obtained. The excitations are localized as well as non-localized. E.g. solitoffs, dromions, multidromions, lumps, breathers, instantons, multivalued solitary waves, doubly periodic waves, etc., can be constructed on the basis of selecting the arbitrary functions properly. Also the interaction properties for all the possible localized excitations are of interest. In this paper, we discuss two elastic interactions. - PACS Ref: 05.45.Yv, 02.30.Jr, 02.30.Ik.

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.

Study of the Solitoff Solution and Fractal Solution for the (2+1)-Dimensional Broek-Kaup System with Variable Coefficients

2014 ◽  
Vol 532 ◽  
pp. 356-361
Author(s):  
Wei Ting Zhu
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Expansion Method ◽  
Variable Coefficients ◽  
Variable Separation ◽  
New Family ◽  
Localized Excitations ◽  
Variable Separation Method

Starting from a (G'/G)-expansion method and a variable separation method, a new family of exact solutions of the (2+1)-dimensional Broek-Kaup system with variable coefficients(VCBK) is obtained. Based on the derived solitary wave solution, we obtain some special localized excitations such as solitoff solutions and fractal solutions.

Study of the Exact Solutions and Chaotic Behaviors in a (2+1)-Dimensional Nonlinear System

2013 ◽  
Vol 340 ◽  
pp. 755-759
Author(s):  
Song Hua Ma
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Water Wave ◽  
Solitary Wave Solution ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Variable Separation Approach

With the help of the symbolic computation system Maple and the (G'/G)-expansion approach and a special variable separation approach, a series of exact solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) of the (2+1)-dimensional modified dispersive water-wave (MDWW) system is derived. Based on the derived solitary wave solution, some novel domino solutions and chaotic patterns are investigated.

SOME NOVEL EVOLUTIONAL BEHAVIORS OF LOCALIZED EXCITATIONS IN THE BOITI–LEON–MARTINA–PEMPINELLI SYSTEM

2008 ◽  
Vol 22 (06) ◽  
pp. 671-682 ◽  
Author(s):  
CHUN-LONG ZHENG ◽  
LI-QUN CHEN
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Bäcklund Transformation ◽  
Backlund Transformation ◽  
Mapping Approach ◽  
Localized Excitations ◽  
Extended Mapping

Using an extended mapping approach and a special Painlevé–Bäcklund transformation, respectively, we obtain two families of exact solutions to the (2+1)-dimensional Boiti–Leon–Martina–Pempinelli (BLMP) system. In terms of the derived exact solution, we reveal some novel evolutional behaviors of localized excitations, i.e., fission, fusion, and annihilation phenomena in the (2+1)-dimensional BLMP system.

Folded Localized Excitations and Chaotic Patterns in a (2+1)-Dimensional Soliton System

2008 ◽  
Vol 63 (3-4) ◽  
pp. 121-126 ◽  
Author(s):  
Song-Hua Ma ◽  
Jian-Ping Fang ◽  
Chun-Long Zheng
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solution ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Localized Excitations ◽  
Dimensional Soliton ◽  
Variable Separation Approach

Starting from an improved mapping approach and a linear variable separation approach, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for the (2+1)-dimensional breaking soliton system are derived. Based on the derived solitary wave solution, we obtain some special folded localized excitations and chaotic patterns.

SINGLE AND MULTIPLE VALUED LOCALIZED EXCITATIONS OF BOITI-LEON-PEMPINELLI SYSTEM IN (2+1)-DIMENSIONS VIA A MAPPING METHOD

2006 ◽  
Vol 20 (22) ◽  
pp. 3233-3245 ◽  
Author(s):  
CHUN-LONG ZHENG ◽  
HAI-PING ZHU ◽  
LIN-SEN XIE ◽  
JIAN-PING FANG
Keyword(s):  
Initial Conditions ◽  
Mapping Method ◽  
Variable Separation ◽  
Mapping Approach ◽  
Localized Excitations ◽  
New Type

With the help of a mapping approach, a new type of variable separation solution with two arbitrary functions to (2+1)-dimensional Boiti–Leon–Pempinelli system (BLP) is derived. Based on the derived variable separation solution, some single valued and multiple valued localized excitations such as dromions, peakons and foldons, etc. with novel evolutional properties are revealed by introducing appropriate initial conditions in this paper.

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