Study on the variable coefficient space–time fractional Korteweg de Vries equation
نویسندگان
چکیده
منابع مشابه
Weakly nonlinear waves in water of variable depth: Variable-coefficient Korteweg-de Vries equation
In the present work, utilizing the two-dimensional equations of an incompressible inviscid fluid and the reductive perturbation method, we studied the propagation of weakly nonlinear waves in water of variable depth. For the case of slowly varying depth, the evolution equation is obtained as a variable-coefficient Korteweg–de Vries (KdV) equation. A progressive wave type of solution, which sati...
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We consider the solitary wave solutions of a Korteweg-de Vries equation, where the coefficients in the equation vary with time over a certain region. When these coefficients vary rapidly compared with the solitary wave, then it is well-known that the solitary wave may fission into two or more solitary waves. On the other hand, when these coefficients vary slowly, the solitary wave deforms adiab...
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We examine the variable-coefficient Kortweg-de Vries equation for the situation when the coefficient of the quadratic nonlinear term changes sign at a certain critical point. This case has been widely studied for a solitary wave, which is extinguished at the critical point and replaced by a train of solitary waves of the opposite polarity to the incident wave, riding on a pedestal of the origin...
متن کاملSymmetry, Integrability and Exact Solutions of a Variable-Coefficient Korteweg-de Vries (vcKdV) Equation
In this paper, a variable-coefficient Korteweg-de Vries (vcKdV) equation which was proposed to describe the propagation of weakly nonlinear waves in water of variable depth is investigated in detail. Firstly, the Lie point symmetries and some group invariant solutions of this equation are presented. Furthermore, the integrability property of this variable-coefficient equation is studied followi...
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In this study, the localfractional variational iterationmethod (LFVIM) and the localfractional series expansion method (LFSEM) are utilized to obtain approximate solutions for Korteweg-de Vries equation (KdVE) within local fractionalderivative operators (LFDOs). The efficiency of the considered methods is illustrated by some examples. The results reveal that the suggested algorithms are very ef...
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ژورنال
عنوان ژورنال: Ain Shams Engineering Journal
سال: 2018
ISSN: 2090-4479
DOI: 10.1016/j.asej.2016.01.013