scholarly journals Travelling wave solutions for a surface wave equation in fluid mechanics

2016 ◽  
Vol 20 (3) ◽  
pp. 893-898 ◽  
Author(s):  
Yi Tian ◽  
Zai-Zai Yan
Keyword(s):  
Wave Equation ◽  
Fluid Mechanics ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Linear Wave ◽  
Travelling Wave Solutions ◽  
Linear Wave Equation ◽  
Wave Solutions

This paper considers a non-linear wave equation arising in fluid mechanics. The exact traveling wave solutions of this equation are given by using G'/G-expansion method. This process can be reduced to solve a system of determining equations, which is large and difficult. To reduce this process, we used Wu elimination method. Example shows that this method is effective.

scholarly journals Computational and traveling wave analysis of Tzitzéica and Dodd-Bullough-Mikhailov equations: An exact and analytical study

2021 ◽  
Vol 10 (1) ◽  
pp. 272-281
Author(s):  
Hülya Durur ◽  
Asıf Yokuş ◽  
Kashif Ali Abro
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Stationary Wave ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Travelling Wave Solutions ◽  
Wave Solutions

Abstract Computational and travelling wave solutions provide significant improvements in accuracy and characterize novelty of imposed techniques. In this context, computational and travelling wave solutions have been traced out for Tzitzéica and Dodd-Bullough-Mikhailov equations by means of (1/G′)-expansion method. The different types of solutions have constructed for Tzitzéica and Dodd-Bullough-Mikhailov equations in hyperbolic form. Moreover, solution function of Tzitzéica and Dodd-Bullough-Mikhailov equations has been derived in the format of logarithmic nature. Since both equations contain exponential terms so the solutions produced are expected to be in logarithmic form. Traveling wave solutions are presented in different formats from the solutions introduced in the literature. The reliability, effectiveness and applicability of the (1/G′)-expansion method produced hyperbolic type solutions. For the sake of physical significance, contour graphs, two dimensional and three dimensional graphs have been depicted for stationary wave. Such graphical illustration has been contrasted for stationary wave verses traveling wave solutions. Our graphical comparative analysis suggests that imposed method is reliable and powerful method for obtaining exact solutions of nonlinear evolution equations.

scholarly journals Exact Traveling Wave Solutions to Benney- Luke Equation

2018 ◽  
Vol 37 ◽  
pp. 1-14
Author(s):  
Zahidul Islam ◽  
Mohammad Mobarak Hossain ◽  
Md Abu Naim Sheikh
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Sobolev Type ◽  
Travelling Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

By using the improved (G¢/G) -expansion method, we obtained some travelling wave solutions of well-known nonlinear Sobolev type partial differential equations, namely, the Benney-Luke equation. We show that the improved (G¢/G) -expansion method is a useful, reliable, and concise method to solve these types of equations.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 1-14

The G′/G-Expansion Method for Solutions of Evolution Equations

2014 ◽  
Vol 940 ◽  
pp. 425-428
Author(s):  
Chun Huan Xiang ◽  
Bo Liang ◽  
Hong Lei Wang
Keyword(s):  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
Nonlinear Problems ◽  
Rational Functions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Trigonometric Functions ◽  
Hyperbolic Functions ◽  
Wave Solutions

The investigation about traveling wave solutions of nonlinear equations is an important and interesting subject because they play important role in understanding the nonlinear problems. By using the (G′/G)-expansion method proposed recently, we construct the travelling wave solutions involving parameters for the Hirota and Satsuma equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The numerical simulation figures are shown.

Bilinear Bäcklund transformation, breather- and travelling-wave solutions for a (2+1)-dimensional extended Kadomtsev–Petviashvili II equation in fluid mechanics

2021 ◽  
pp. 2150315
Author(s):  
Yong-Xin Ma ◽  
Bo Tian ◽  
Qi-Xing Qu ◽  
He-Yuan Tian ◽  
Shao-Hua Liu
Keyword(s):  
Fluid Mechanics ◽  
Bäcklund Transformation ◽  
Expansion Method ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Backlund Transformation ◽  
Bilinear Method ◽  
Test Technique ◽  
Wave Solutions ◽  
Bilinear Bäcklund Transformation

Fluid-mechanics studies are applied in mechanical engineering, biomedical engineering, oceanography, meteorology and astrophysics. In this paper, we investigate a (2+1)-dimensional extended Kadomtsev–Petviashvili II equation in fluid mechanics. Based on the Hirota bilinear method, we give a bilinear Bäcklund transformation. Via the extended homoclinic test technique, we construct the breather-wave solutions under certain constraints. We obtain the velocities of the breather waves, which depend on the coefficients in that equation. Besides, we derive the lump solutions with the periods of the breather-wave solutions tending to the infinity. Based on the polynomial-expansion method, travelling-wave solutions are constructed. We observe that the shapes of a breather wave and a lump remain unchanged during the propagation. We graphically discuss the effects of those coefficients on the breather wave and lump.

scholarly journals Travelling Wave Solutions for Two Generalized Hirota-Satsuma Coupled KdV Systems

2001 ◽  
Vol 56 (3-4) ◽  
pp. 312-318 ◽  
Author(s):  
Engui Fan
Keyword(s):  
Full Advantage ◽  
Riccati Equation ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Symbolic Computations ◽  
Extended Tanh Method ◽  
Wave Solutions ◽  
Tanh Method

Abstract In this paper we present an extended tanh method that utilizes symbolic computations to obtain more travelling wave solutions for two generalized Hirota-Satsuma coupled KdV systems in a unified way. The key idea of this method is to take full advantage of a Riccati equation involving a parameter and use its solutions to replace the tanh-function by the tanh method. It is quite interesting that the numbers and types of the traveling wave solutions can be judged from the sign of the parameter. In this paper we investigate the two generalized Hirota-Satsuma coupled KdV systems

scholarly journals Fundamental solutions for the long–short-wave interaction system

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1093-1099
Author(s):  
Mustafa Inc ◽  
Samia Zaki Hassan ◽  
Mahmoud Abdelrahman ◽  
Reem Abdalaziz Alomair ◽  
Yu-Ming Chu
Keyword(s):  
Fluid Mechanics ◽  
Traveling Wave ◽  
Inverse Method ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Wave Interaction ◽  
Fundamental Solutions ◽  
Short Wave ◽  
Wave Solutions ◽  
Physical Environments

Abstract In this article, the system for the long–short-wave interaction (LS) system is considered. In order to construct some new traveling wave solutions, He’s semi-inverse method is implemented. These solutions may be applicable for some physical environments, such as physics and fluid mechanics. These new solutions show that the proposed method is easy to apply and the proposed technique is a very powerful tool to solve many other nonlinear partial differential equations in applied science.

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