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.

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.

General variable separation solution and new localized excitations for the (2 + 1)-dimensional nonlinear Schrödinger equation

2006 ◽  
Vol 84 (12) ◽  
pp. 1107-1123
Author(s):  
Cheng -Lin Bai ◽  
Hai -Quan Hu ◽  
Wen -Jun Wang ◽  
Hong Zhao
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bäcklund Transformation ◽  
Nonlinear Schrodinger Equation ◽  
Variable Separation ◽  
Backlund Transformation ◽  
Nonlinear Schrödinger ◽  
New Class ◽  
Localized Excitations

By applying a special Bäcklund transformation, a general variable separation solution for the (2 + 1)-dimensional nonlinear Schrödinger equation is derived. In addition to some types of the usual localized excitations, such as dromions, lumps, ring solitons, oscillated dromions, and breathers, soliton structures can be easily constructed by selecting arbitrary functions appropriately. A new class of localized excitations, like fractal-dromions, fractal-lumps, peakons, compactons, and folded excitations of this system is found by selecting appropriate functions. Some interesting novel features of these structures are revealed.PACS Nos.: 05.45.–a, 02.30.Jr

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.

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.

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.

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