Equivalence groupoid of a class of variable coefficient Korteweg–de Vries equations
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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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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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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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2017
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.5004973