Travelling wave solutions for a second order wave equation of KdV type

AbstractIn this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The solutions are obtained by using a two-step factorization procedure through which the perturbed KdV equation is reduced to a nonlinear second order differential equation, and to some Bernoulli and Abel type differential equations whose solutions are expressed in terms of the exponential andWeierstrass functions.

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Some new travelling wave solutions with singular or nonsingular character for the higher order wave equation of KdV type (III)

Nonlinear Analysis ◽

10.1016/j.na.2008.07.040 ◽

2009 ◽

Vol 70 (11) ◽

pp. 3816-3828 ◽

Cited By ~ 10

Author(s):

Weiguo Rui ◽

Yao Long ◽

Bin He

Keyword(s):

Wave Equation ◽

Travelling Wave ◽

Higher Order ◽

Travelling Wave Solutions ◽

Type Iii ◽

Wave Solutions

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Elliptic Travelling Wave Solutions to a Generalized Boussinesq Equation

Abstract and Applied Analysis ◽

10.1155/2014/256019 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7

Author(s):

Abdelfattah El Achab

Keyword(s):

Wave Equation ◽

Elliptic Function ◽

Function Method ◽

Boussinesq Equation ◽

Travelling Wave ◽

Travelling Wave Solutions ◽

Weierstrass Elliptic Function ◽

Wave Solutions ◽

Generalized Boussinesq Equation

Travelling wave solutions for the generalized Boussinesq wave equation are studied by using the Weierstrass elliptic function method. As a result, some previously known solutions are recovered, and at the same time some new ones are also given, as well as integrable ones.

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Travelling wave solutions for a surface wave equation in fluid mechanics

Thermal Science ◽

10.2298/tsci1603893t ◽

2016 ◽

Vol 20 (3) ◽

pp. 893-898 ◽

Cited By ~ 1

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.

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Travelling Wave solutions of hyperbolic Telegraph equation by Tanh method

Turkish Journal of Computer and Mathematics Education (TURCOMAT) ◽

10.17762/turcomat.v12i2.2344 ◽

2021 ◽

Vol 12 (2) ◽

pp. 3032-3035

Author(s):

Anjali Verma, Et. al.

Keyword(s):

Differential Equations ◽

Nonlinear Differential Equations ◽

Telegraph Equation ◽

Travelling Wave ◽

Second Order ◽

Travelling Wave Solutions ◽

Wave Solutions ◽

Tanh Method ◽

Convenient Approach ◽

Nonlinear Telegraph Equation

Tanh method is utilized to find travelling solutions of second order nonlinear Telegraph equation. As a result, we attain dissimilar travelling wave solutions. Our aim is to show that this method is most efficient and convenient approach for verdict travelling wave solutions of nonlinear differential equations. For calculation the software MAPLE is used.

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