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.

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.

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

Painlevé Integrability and Abundant Localized Structures of (2+1)-dimensional Higher Order Broer-Kaup System

2002 ◽  
Vol 57 (12) ◽  
pp. 929-936 ◽  
Author(s):  
Ji Lin ◽  
Hua-mei Li
Keyword(s):  
Phase Shift ◽  
Coherent Structures ◽  
Higher Order ◽  
Separation Method ◽  
Variable Separation ◽  
Localized Structures ◽  
Painlevé Property ◽  
Variable Separation Method ◽  
Truncated Painlevé Expansion

It is proven that the (2+1) dimensional higher-order Broer-Kaup system the possesses the Painlevé property, using the Weiss-Tabor-Carnevale method and Kruskal’s simplification. Abundant localized coherent structures are obtained by using the standard truncated Painlevé expansion and the variable separation method. Fractal dromion solutions and multi-peakon structures are discussed. The interactions of three peakons are investigated. The interactions among the peakons are not elastic; they interchange their shapes but there is no phase shift

Symbolic Computation and Non-travelling Wave Solutions of the (2+1)-Dimensional Korteweg de Vries Equation

2005 ◽  
Vol 60 (4) ◽  
pp. 221-228 ◽  
Author(s):  
Dengshan Wang ◽  
Hong-Qing Zhang
Keyword(s):  
Symbolic Computation ◽  
Evolution Equations ◽  
Vries Equation ◽  
Expansion Method ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Jacobi Elliptic Function ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
De Vries

Abstract In this paper, with the aid of symbolic computation we improve the extended F-expansion method described in Chaos, Solitons and Fractals 22, 111 (2004) to solve the (2+1)-dimensional Korteweg de Vries equation. Using this method, we derive many exact non-travelling wave solutions. These are more general than the previous solutions derived with the extended F-expansion method. They include the Jacobi elliptic function, soliton-like trigonometric function solutions, and so on. Our method can be applied to other nonlinear evolution equations.

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.

scholarly journals Exact Solutions for the Wick-Type Stochastic Schamel-Korteweg-de Vries Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Xueqin Wang ◽  
Yadong Shang ◽  
Huahui Di
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Vries Equation ◽  
Expansion Method ◽  
Travelling Wave ◽  
Variable Coefficients ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
De Vries ◽  
Hermite Transformation

We consider the Wick-type stochastic Schamel-Korteweg-de Vries equation with variable coefficients in this paper. With the aid of symbolic computation and Hermite transformation, by employing the (G′/G,1/G)-expansion method, we derive the new exact travelling wave solutions, which include hyperbolic and trigonometric solutions for the considered equations.

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