scholarly journals Multidromion Soliton and Rouge Wave for the (2 + 1)-Dimensional Broer-Kaup System with Variable Coefficients

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Zitian Li
Keyword(s):  
Variable Coefficients ◽  
Variable Separation ◽  
Rational Form ◽  
Localized Solutions ◽  
Mapping Approach ◽  
Rouge Wave ◽  
Lower Dimensional

Broad new families of rational form variable separation solutions with two arbitrary lower-dimensional functions of the (2 + 1)-dimensional Broer-Kaup system with variable coefficients are derived by means of an improved mapping approach and a variable separation hypothesis. Based on the derived variable separation excitation, some new special types of localized solutions such as rouge wave, multidromion soliton, and soliton vanish phenomenon are revealed by selecting appropriate functions of the general variable separation solution.

scholarly journals Diversity soliton excitations for the (2+1)-dimensional Schwarzian Korteweg-de Vries equation

2018 ◽  
Vol 22 (4) ◽  
pp. 1781-1786 ◽  
Author(s):  
Zitian Li
Keyword(s):  
Symbolic Computation ◽  
Coherent Structures ◽  
Vries Equation ◽  
Qualitative Behavior ◽  
Variable Separation ◽  
Wave Type ◽  
Localized Structures ◽  
Mapping Approach ◽  
De Vries ◽  
Rouge Wave

With the aid of symbolic computation, we derive new types of variable separation solutions for the (2+1)-dimensional Schwarzian Korteweg-de Vries equation based on an improved mapping approach. Rich coherent structures like the soliton-type, rouge wave-type, and cross-like fractal type structures are presented, and moreover, the fusion interactions of localized structures are graphically investigated. Some of these solutions exhibit a rich dynamic, with a wide variety of qualitative behavior and structures that are exponentially localized.

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.

scholarly journals Exact solutions of time fractional heat-like and wave-like equations with variable coefficients

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 689-693 ◽  
Author(s):  
Sheng Zhang ◽  
Ran Zhu ◽  
Luyao Zhang
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Variable Coefficient ◽  
Variable Coefficients ◽  
Separation Method ◽  
Variable Separation ◽  
Science And Engineering ◽  
Special Solutions ◽  
Initial And Boundary Conditions ◽  
Variable Separation Method

In this paper, a variable-coefficient time fractional heat-like and wave-like equation with initial and boundary conditions is solved by the use of variable separation method and the properties of Mittag-Leffler function. As a result, exact solutions are obtained, from which some known special solutions are recovered. It is shown that the variable separation method can also be used to solve some others time fractional heat-like and wave-like equation in science and engineering.

Painlevé Integrability and a New Exact Solution of the Multi-Component Sasa-Satsuma Equation

2015 ◽  
Vol 70 (10) ◽  
pp. 823-828 ◽  
Author(s):  
Yujian Ye ◽  
Danda Zhang ◽  
Yanmei Di
Keyword(s):  
Exact Solution ◽  
Physical Quantity ◽  
Coherent Structure ◽  
Variable Separation ◽  
Variable Separation Approach ◽  
Lower Dimensional

AbstractIn this article, Painlevé integrability of the multi-component Sasa-Satsuma equation is confirmed by using the standard WTC approach and the Kruskal simplification. Then, by means of the multi-linear variable separation approach, a new exact solution with lower-dimensional arbitrary functions is constructed. For the physical quantity $U\; = \;\sum\nolimits_{i\; = \;1}^N \sum\nolimits_{j\; = \;i}^N {a_{ij}}{p_i}{p_j}\; = \; - \;\frac{3}{{2\beta }}\frac{{{F_x}{G_y}}}{{{{(F\; + \;G)}^2}}},$ new coherent structure which possesses peakons at x-axis and compactons at y-axis is illustrated both analytically and graphically.

NEW SOLITARY WAVE AND JACOBI PERIODIC WAVE EXCITATIONS IN (2+1)-DIMENSIONAL BOITI–LEON–MANNA–PEMPINELLI SYSTEM

2008 ◽  
Vol 22 (15) ◽  
pp. 2407-2420 ◽  
Author(s):  
CHENG-JIE BAI ◽  
HONG ZHAO
Keyword(s):  
General Solution ◽  
Solitary Wave ◽  
Elliptic Functions ◽  
Periodic Wave ◽  
Jacobi Elliptic Functions ◽  
Variable Separation ◽  
Smooth Functions ◽  
Localized Structures ◽  
Variable Separation Approach ◽  
Lower Dimensional

By means of the multilinear variable separation approach, a general variable separation solution of the Boiti–Leon–Manna–Pempinelli equation is derived. Based on the general solution, some new types of localized structures — compacton and Jacobi periodic wave excitations are obtained by introducing appropriate lower-dimensional piecewise smooth functions and Jacobi elliptic functions.

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.

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

Novel Excitations of the Nonlinear Schrödinger Equation by Separation of Variables

2009 ◽  
Vol 64 (1-2) ◽  
pp. 21-29 ◽  
Author(s):  
Xian-Jing Lai ◽  
Jie-Fang Zhang
Keyword(s):  
Separation Of Variables ◽  
Variable Separation ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Localized Solutions ◽  
Extended Tanh Method ◽  
Straight Line ◽  
Tanh Method ◽  
New Type ◽  
Line Soliton

By means of an extended tanh method, a new type of variable separation solutions with two arbitrary lower-dimensional functions of the (2+1)-dimensional nonlinear Schrödinger (NLS) equation is derived. Based on the derived variable separation excitation, some special types of localized solutions such as a curved soliton, a straight-line soliton and a periodic soliton are constructed by choosing appropriate functions. In addition, one dromion changes its shape during the collision with a folded solitary wave.

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