Study of the New Solitory Wave Solutions and Periodic Wave Solutions of a Two-Dimensional Modified KdV Equation

2013 ◽  
Vol 432 ◽  
pp. 122-126
Author(s):  
Mei Ling Gu ◽  
Zhi Hua Zhu ◽  
Song Hua Ma
Keyword(s):  
Kdv Equation ◽  
Periodic Wave ◽  
Mkdv Equation ◽  
Separation Method ◽  
Two Dimensional ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Modified Kdv Equation ◽  
Variable Separation Method

With the help of the Riccati mapping approach and the variable separation method, some new solitory wave solutions and periodic wave solutions of the two-dimensional modified KdV(MKdV) equation are derived.

Solitary Wave and Periodic Wave Solutions and Chaotic Behaviors in a (2+1)-Dimensional Nonlinear System

2014 ◽  
Vol 532 ◽  
pp. 346-350
Author(s):  
Xiao Xin Zhu ◽  
Song Hua Ma ◽  
Qing Bao Ren
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solution ◽  
Periodic Wave ◽  
Mapping Method ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Variable Separation Method

With the help of the symbolic computation system Maple and an improved mapping method and a variable separation method, a series of new exact solutions (including solitary wave solutions and periodic wave solutions) to the (2+1)-dimensional general Nizhnik-Novikov-Veselov (GNNV) system is derived. Based on the derived solitary wave solution, we obtain some chaotic patterns.

Investigation of (G'/G)-Expansion Method and Exact Solutions for the (2+1)-Dimensional Calogero-Bogoyavlenskii-Schiff System

2013 ◽  
Vol 432 ◽  
pp. 235-239
Author(s):  
Gen Hai Xu ◽  
Song Hua Ma ◽  
Jian Ping Fang
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
New Family ◽  
Wave Solutions ◽  
Variable Separation Method

With the help of the symbolic computation system Maple and the (G'/G)-expansion method and a linear variable separation method, a new family of exact solutions (including solitary wave solutions,periodic wave solutions and rational function solutions) of the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff system (2DCBS) is derived.

Study of the New Exact Solutions of a (3+1)-Dimensional Nonlinear Evolution Equation

2012 ◽  
Vol 268-270 ◽  
pp. 1182-1185
Author(s):  
Ma Biao Zhang
Keyword(s):  
Nonlinear Evolution Equation ◽  
Water Wave ◽  
Nonlinear Evolution ◽  
Solitary Wave Solution ◽  
Periodic Wave ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Variable Separation Method

By the symbolic computation system Maple and the Riccati mapping approach and a variable separation method, some new variable separation solutions ( including solitory wave solutions and periodic wave solutions ) of the (3+1)-dimensional generalized shallow water wave (3DWW) system are derived. Based on the derived solitary wave solution, some novel solitoff solutions are investigated.

Lump-type solutions, interaction solutions and periodic wave solutions of a (3+1)-dimensional Korteweg–de Vries equation

2019 ◽  
Vol 33 (27) ◽  
pp. 1950319 ◽  
Author(s):  
Hongfei Tian ◽  
Jinting Ha ◽  
Huiqun Zhang
Keyword(s):  
Vries Equation ◽  
Kdv Equation ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Interaction Solutions ◽  
Dynamical Behaviors ◽  
Wave Solutions ◽  
Hirota Bilinear Form ◽  
De Vries ◽  
Hirota Bilinear

Based on the Hirota bilinear form, lump-type solutions, interaction solutions and periodic wave solutions of a (3[Formula: see text]+[Formula: see text]1)-dimensional Korteweg–de Vries (KdV) equation are obtained. The interaction between a lump-type soliton and a stripe soliton including two phenomena: fission and fusion, are illustrated. The dynamical behaviors are shown more intuitively by graphics.

EXACT SOLITON SOLUTIONS AND QUASI-PERIODIC WAVE SOLUTIONS TO THE FORCED VARIABLE-COEFFICIENT KdV EQUATION

2012 ◽  
Vol 26 (19) ◽  
pp. 1250072 ◽  
Author(s):  
YI ZHANG ◽  
ZHILONG CHENG
Keyword(s):  
Variable Coefficient ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Time Dependent ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Hirota Bilinear ◽  
Exact Soliton Solutions

In this paper, the time-dependent variable-coefficient KdV equation with a forcing term is considered. Based on the Hirota bilinear method, the bilinear form of this equation is obtained, and the multi-soliton solutions are studied. Then the periodic wave solutions are obtained by using Riemann theta function, and it is also shown that classical soliton solutions can be reduced from the periodic wave solutions.

scholarly journals Time Evolution of Folded (2+1)-Dimensional Solitary Waves

2009 ◽  
Vol 64 (5-6) ◽  
pp. 309-314 ◽  
Author(s):  
Song-Hua Ma ◽  
Yi-Pin Lu ◽  
Jian-Ping Fang ◽  
Zhi-Jie Lv
Keyword(s):  
Solitary Wave ◽  
Elliptic Function ◽  
Water Wave ◽  
Periodic Wave ◽  
Wave System ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Variable Separation Approach

Abstract With an extended mapping approach and a linear variable separation approach, a series of solutions (including theWeierstrass elliptic function solutions, solitary wave solutions, periodic wave solutions and rational function solutions) of the (2+1)-dimensional modified dispersive water-wave system (MDWW) is derived. Based on the derived solutions and using some multi-valued functions, we find a few new folded solitary wave excitations.

scholarly journals Numerical calculation of N -periodic wave solutions to coupled KdV–Toda-type equations

2021 ◽  
Vol 477 (2245) ◽  
pp. 20200752
Author(s):  
Yingnan Zhang ◽  
Xingbiao Hu ◽  
Jianqing Sun
Keyword(s):  
Toda Lattice ◽  
Kdv Equation ◽  
Direct Method ◽  
Periodic Wave ◽  
Periodic Waves ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Numerical Process ◽  
Relativistic Toda Lattice ◽  
Ito Equation

In this paper, we study the N -periodic wave solutions of coupled Korteweg–de Vries (KdV)–Toda-type equations. We present a numerical process to calculate the N -periodic waves based on the direct method of calculating periodic wave solutions proposed by Akira Nakamura. Particularly, in the case of N  = 3, we give some detailed examples to show the N -periodic wave solutions to the coupled Ramani equation, the Hirota–Satsuma coupled KdV equation, the coupled Ito equation, the Blaszak–Marciniak lattice, the semi-discrete KdV equation, the Leznov lattice and a relativistic Toda lattice.

Study of the Exact Solutions and Chaotic Behaviors in a (2+1)-Dimensional Nonlinear System

2013 ◽  
Vol 340 ◽  
pp. 755-759
Author(s):  
Song Hua Ma
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Water Wave ◽  
Solitary Wave Solution ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Variable Separation Approach

With the help of the symbolic computation system Maple and the (G'/G)-expansion approach and a special variable separation approach, a series of exact solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) of the (2+1)-dimensional modified dispersive water-wave (MDWW) system is derived. Based on the derived solitary wave solution, some novel domino solutions and chaotic patterns are investigated.

scholarly journals Exact Peakon, Compacton, Solitary Wave, and Periodic Wave Solutions for a Generalized KdV Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-19
Author(s):  
Qing Meng ◽  
Bin He
Keyword(s):  
Dynamical System ◽  
Numerical Simulation ◽  
Solitary Wave ◽  
Planar Graphs ◽  
Kdv Equation ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Generalized Kdv Equation ◽  
Wave Solutions ◽  
Periodic Cusp Waves

We employ the approaches of both dynamical system and numerical simulation to investigate a generalized KdV equation, which is presented by Yin (2012). Some peakon, compacton, solitary wave, smooth periodic wave, and periodic cusp wave solutions are obtained, and the planar graphs of the compactons and the periodic cusp waves are simulated.

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