scholarly journals Solitary wave series solution for generalized (3+1)-dimensional nonlinear Burgers system

2010 ◽  
Vol 59 (12) ◽  
pp. 8311
Author(s):  
Mo Jia-Qi ◽  
Wen Zhao-Hui
Keyword(s):  
Solitary Wave ◽  
Series Solution ◽  
Burgers System

Bell Waves and Kind Waves for a (1+1)-Dimensional Nonlinear Partial Differential Equation

2013 ◽  
Vol 273 ◽  
pp. 831-834
Author(s):  
Qing Bao Ren ◽  
Song Hua Ma ◽  
Jian Ping Fang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Solitary Wave ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Nonlinear Partial Differential Equation ◽  
Variable Separation ◽  
New Family ◽  
Variable Separation Approach ◽  
Burgers System

With the help of the symbolic computation system Maple and the mapping approach and a linear variable separation approach, a new family of exact solutions of the (1+1)-dimensional Burgers system is derived. Based on the derived solitary wave solution, some novel bell wave and kind wave excitations are investigated.

scholarly journals Solitary Wave-Series Solutions to Non-Linear Schrodinger Equations

2012 ◽  
Vol 13 (1) ◽  
Author(s):  
Muhammad Azram ◽  
H. Zaman
Keyword(s):  
Solitary Wave ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Series Solution ◽  
Higher Order ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Series Solutions ◽  
Non Linear ◽  
Continuity And Discontinuity

ABSTRACT: In this paper, higher-order dispersive non-linear Schrodinger equations are studied. Their solitary wave-series solutions with continuity of the derivatives and specific discontinuity of the derivatives at the crest are presented. Furthermore, convergence of the series’ solutions is also validated and discussed with the help of graphs. ABSTRAK: Kertas ini mengkaji persamaan Schrodinger serakan taklinear turutan tinggi. Penyelesaian siri-gelombang tunggalnya dengan kamiran berterusan dan kamiran tak berterusan pada maksimum telah dibentangkan. Penumpuan penyelesaian siri juga telah diperiksa dan dibincangkan dengan bantuan graf-graf.KEYWORDS: Schrodinger equation; solitary wave-series solution; continuity and discontinuity of derivatives at crest

scholarly journals THE EXACT SOLUTION OF THE HIGHEST WAVE DERIVED FROM A UNIVERSAL WAVE MODEL

1984 ◽  
Vol 1 (19) ◽  
pp. 70
Author(s):  
Yang Yih Chen ◽  
Frederick L.W. Tang
Keyword(s):  
Exact Solution ◽  
Solitary Wave ◽  
Gravity Wave ◽  
Wave Height ◽  
Water Depth ◽  
Series Solution ◽  
Wave Model ◽  
Finite Depth

The solitary wave is first established in this paper by extending the series solution of periodic gravity wave as the wavelength approaches to infinite. Then, the highest gravity wave of permanent type in finite depth of water is immediately analyzed. The maximum ratio of wave height to water depth is obtained as 0.85465')..., and the angle at the crest for the considered highest wave is estimated to be 90°.

A note on the series solution of the solitary wave problem

2002 ◽  
Vol 154 (1-4) ◽  
pp. 233-242
Author(s):  
L. Engevik
Keyword(s):  
Solitary Wave ◽  
Series Solution ◽  
Wave Problem

scholarly journals Construction of New Exact Solutions for the (3 + 1)-Dimensional Burgers System

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Zitian Li
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Separation Method ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Kink Wave ◽  
Variable Separation Method ◽  
Burgers System

By means of a variable separation method and a generalized direct ansätz function approach, new exact solutions including cross kink-wave solutions, doubly periodic kinky-wave solutions, and breather type of two-solitary wave solutions for the (3 + 1)-dimensional Burgers system are obtained. Moreover, the mechanical features are also investigated.

On the Exact Soliton Solutions of Some Nonlinear PDE by Tan-Cot Method

2018 ◽  
Vol 5 (1) ◽  
pp. 31-36
Author(s):  
Md Monirul Islam ◽  
Muztuba Ahbab ◽  
Md Robiul Islam ◽  
Md Humayun Kabir
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Rectangular Channel ◽  
Soliton Solutions ◽  
Boussinesq Equations ◽  
Travelling Wave ◽  
Ion Acoustic Waves ◽  
Analytical System

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36

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