scholarly journals Constructions of solitary travelling wave solutions for Ito integro-differential equation arising in plasma physics

2020 ◽  
Vol 19 ◽  
pp. 103533
Author(s):  
Abdulghani R. Alharbi ◽  
M.B. Almatrafi ◽  
Kh. Lotfy
Keyword(s):  
Differential Equation ◽  
Plasma Physics ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Integro Differential Equation ◽  
Wave Solutions ◽  
Solitary Travelling Wave

scholarly journals Solutions of the perturbed KdV equation for convecting fluids by factorizations

Open Physics ◽  
2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Octavio Cornejo-Pérez ◽  
Haret Rosu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Kdv Equation ◽  
Travelling Wave ◽  
Second Order ◽  
Travelling Wave Solutions ◽  
Second Order Differential Equation ◽  
Wave Solutions ◽  
Perturbed Kdv Equation

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.

New Exact Travelling Wave Solutions of Nonlinear Coagulation Problem with Mass Loss

2010 ◽  
Vol 65 (3) ◽  
pp. 209-214
Author(s):  
El-Said A. El-Wakil ◽  
Essam M. Abulwafa ◽  
Mohammed A. Abdou
Keyword(s):  
Differential Equation ◽  
Mass Loss ◽  
Evolution Equations ◽  
Expansion Method ◽  
Approximate Solutions ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Travelling Wave Solutions ◽  
Rational Solutions ◽  
Wave Solutions

This paper suggests a generalized F-expansion method for constructing new exact travelling wave solutions of a nonlinear coagulation problem with mass loss. This method can be used as an alternative to obtain analytical and approximate solutions of different types of kernel which are applied in physics. The nonlinear kinetic equation, which is an integro differential equation, is transformed into a differential equation using Laplace’s transformation. The inverse Laplace transformation of the solution gives the size distribution function of the system. As a result, many exact travelling wave solutions are obtained which include new periodic wave solutions, trigonometric function solutions, and rational solutions. The method is straightforward and concise,and it can also be applied to other nonlinear evolution equations arising in mathematical physics.

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