Exact solutions of a generalized (2+1)-dimensional soliton equation via Bell polynomials

2021 ◽  
Author(s):  
Dan Wang ◽  
Shu-Li Liu ◽  
Yong Geng ◽  
Xiao-Li Wang
Keyword(s):  
Exact Solutions ◽  
Bell Polynomials ◽  
Soliton Equation ◽  
Dimensional Soliton

Exact Solutions and Solitons with Fission and Fusion Properties for the Generalized Broer-Kaup System

2006 ◽  
Vol 61 (1-2) ◽  
pp. 16-22
Author(s):  
Chun-Long Zheng ◽  
Jian-Ping Fang
Keyword(s):  
Exact Solutions ◽  
Variable Separation ◽  
Soliton Fission ◽  
Dimensional Soliton ◽  
Variable Separation Approach ◽  
03.65 Ge

Starting from a Painlev´e-B¨acklund transformation and a linear variable separation approach, we obtain a quite general variable separation excitation to the generalized (2+1)-dimensional Broer-Kaup (GBK) system. Then based on the derived solution, we reveal soliton fission and fusion phenomena in the (2+1)-dimensional soliton system. - PACS numbers: 05.45.Yv, 03.65.Ge

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.

Traveling Wave Solution of (2+1) Dimensional Breaking Soliton Equation by Bernoulli Sub-ODE Method

2011 ◽  
Vol 403-408 ◽  
pp. 207-211
Author(s):  
Qing Hua Feng ◽  
Yu Lu Wang
Keyword(s):  
Exact Solutions ◽  
Nonlinear Equations ◽  
Traveling Wave ◽  
Wave Solution ◽  
Present Method ◽  
Expansion Method ◽  
Traveling Wave Solution ◽  
Soliton Equation ◽  
Ode Method

In this paper, we derive exact traveling wave soluti-ons of (2+1) dimensional breaking soliton equation by a proposed Bernoulli sub-ODE method. The method appears to be efficient in seeking exact solutions of nonlinear equations. We also make a comparison between the present method and the known (G’/G) expansion method.

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 Localized Excitations in a (2+1)-Dimensional Soliton System

2009 ◽  
Vol 64 (1-2) ◽  
pp. 37-43
Author(s):  
Song-Hua Ma ◽  
Jian-Ping Fang
Keyword(s):  
Exact Solutions ◽  
Water Wave ◽  
Reduction Method ◽  
Wave System ◽  
Similarity Reduction ◽  
New Exact Solutions ◽  
Localized Excitations ◽  
Reduction Equation ◽  
Dimensional Soliton

Starting from a special conditional similarity reduction method, we obtain the reduction equation of the (2+1)-dimensional dispersive long-water wave system. Based on the reduction equation, some new exact solutions and abundant localized excitations are obtained.

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