scholarly journals Construction of lump soliton and mixed lump stripe solutions of (3+1)-dimensional soliton equation

2018 ◽  
Vol 10 ◽  
pp. 94-98 ◽  
Author(s):  
Jiangen Liu ◽  
Yufeng Zhang
Keyword(s):  
Soliton Equation ◽  
Dimensional Soliton

THE NONLINEARIZATION OF A (2+1)-DIMENSIONAL SOLITON EQUATION

2008 ◽  
Vol 22 (32) ◽  
pp. 3179-3194
Author(s):  
QIANG LIU ◽  
DIAN-LOU DU
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Hamiltonian System ◽  
Eigenvalue Problem ◽  
Hamiltonian Systems ◽  
Soliton Equation ◽  
Completely Integrable ◽  
Finite Dimensional ◽  
Dimensional Soliton

Based on a 2 × 2 eigenvalue problem, a new (2+1)-dimensional soliton equation is proposed. Moreover, we obtain a finite-dimensional Hamiltonian system. Then we verify it is completely integrable in the Liouville sense. In the end, we introduce a set of Hk polynomial integrable, by which we can separate the solition equation into three compantiable Hamiltonian systems of ordinary differential equation.

scholarly journals A Study on Lump and Interaction Solutions to a (3 + 1)-Dimensional Soliton Equation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Xi-zhong Liu ◽  
Zhi-Mei Lou ◽  
Xian-Min Qian ◽  
Lamine Thiam
Keyword(s):  
Interaction Process ◽  
Lump Solution ◽  
Soliton Equation ◽  
Lump Solutions ◽  
Interaction Solutions ◽  
Finite Period ◽  
Bilinear Formulation ◽  
Dimensional Soliton

Based on bilinear formulation of a (3 + 1)-dimensional soliton equation, lump solution and related interaction solutions are investigated. The lump solutions of the soliton equation are classified into three cases with nonsingularity conditions being given. The interaction solutions between lump and a stripe soliton are obtained in eight cases, which have interesting fusing and fission behaviors with changing time. The interaction solutions of the soliton equation between a lump and a resonant pair of stripe solitons are also given, and we find that the lump just exist for a finite period during the interaction process.

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.

Exotic Localized Coherent Structures of New (2+1)-Dimensional Soliton Equation

2002 ◽  
Vol 38 (5) ◽  
pp. 517-522 ◽  
Author(s):  
Zhang Jie-Fang ◽  
Huang Wen-Hua ◽  
Zheng Chun-Long
Keyword(s):  
Coherent Structures ◽  
Soliton Equation ◽  
Dimensional Soliton
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