Rich Localized Coherent Structures of the (2+1)-Dimensional BKK Equation

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4247-4251 ◽  
Author(s):  
H. M. Li ◽  
S. Y. Lou
Keyword(s):  
Coherent Structures ◽  
Arbitrary Function ◽  
Bäcklund Transformation ◽  
Variable Separation ◽  
Backlund Transformation ◽  
Seed Solution ◽  
Localized Structures ◽  
Variable Separation Approach

Using a Bäcklund transformation and the variable separation approach, we find there exist rich localized structures for the (2+1)-dimensional Broer-Kaup-Kupershmidt (BKK) system. The abundance of the localized structures for the model is introduced by the entrance of an arbitrary function of the seed solution. For some special selections of the arbitrary function, it is shown that the localized structure of the BKK equation may be dromions, lumps, ring solitons and peakons etc.

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.

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.

GENERAL VARIABLE SEPARATION SOLUTION AND EXOTIC LOCALIZED STRUCTURES OF NEW (2+1)-DIMENSIONAL SOLITON EQUATION

2005 ◽  
Vol 19 (12) ◽  
pp. 2011-2044 ◽  
Author(s):  
CHENG-LIN BAI ◽  
CHENG-JIE BAI ◽  
HONG ZHAO
Keyword(s):  
Bäcklund Transformation ◽  
Variable Separation ◽  
Backlund Transformation ◽  
Soliton Equation ◽  
Localized Structures ◽  
New Novel ◽  
Localized Excitations ◽  
Dimensional Soliton

By applying a special Bäcklund transformation, a quite general variable separation solution for new (2+1)-dimensional soliton equation is derived. In addition to some types of the usual localized excitations such as dromion, lumps, ring soliton, oscillated dromion and breathers soliton structures can be easily constructed by selecting the arbitrary functions appropriately, a new novel class of localized structures like fractal-dromion, fractal-lump, peakon, compacton and folded excitation of this system are found by selecting appropriate functions. Some interesting novel features of these structures are revealed.

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

EXACT SOLUTIONS AND COMPLEX WAVE EXCITATIONS OF GENERALIZED SASA–SATSUMA SYSTEM IN (2+1)-DIMENSIONS

2009 ◽  
Vol 23 (19) ◽  
pp. 3931-3938 ◽  
Author(s):  
CHUN-LONG ZHENG ◽  
JIAN-FENG YE
Keyword(s):  
Exact Solutions ◽  
Solitary Waves ◽  
Bäcklund Transformation ◽  
Periodic Wave ◽  
Variable Separation ◽  
Backlund Transformation ◽  
Complex Wave

Starting from a Painlevé–Bäcklund transformation, an exact variable separation solution with four arbitrary functions for the (2+1)-dimensional generalized Sasa–Satsuma (GSS) system are derived. Based on the derived exact solutions in the paper, some complex wave excitations in the (2+1)-dimensional GSS system and revealed, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave background are also briefly discussed.

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.

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.

New Multi-Soliton Solutions of the (2+1)-Dimensional Breaking Soliton Equations

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4376-4381 ◽  
Author(s):  
Jie-Fang Zhang ◽  
Chun-Long Heng
Keyword(s):  
Bäcklund Transformation ◽  
Direct Method ◽  
Soliton Solutions ◽  
Variable Separation ◽  
Backlund Transformation ◽  
Soliton Equations ◽  
Simplified Form

A simple and direct method is used to solve the (2+1)-dimensional breaking soliton equations: qt=iqxy-2iq∫(qr)ydx, rt=-irxy+2ir∫(qr)ydx. This technique yields a simplified form of the (2+1)-dimensional breaking soliton equations by use of a special Bäcklund transformation and a variable separation solution of this model is derived. Some special types of multi-soliton structure are constructed by selecting the arbitrary functions and arbitrary constants appropriately.

Sign in / Sign up

Export Citation Format

Share Document