On rational similarity solutions of $KdV$ and $m$-$KdV$ equations
نویسندگان
چکیده
منابع مشابه
Rational solutions to a KdV-like equation
Two classes of rational solutions to a KdV-like nonlinear differential equation are constructed. The basic object is a generalized bilinear differential equation based on a prime number p 1⁄4 3. A conjecture is made that the two presented classes of rational solutions contain all rations solutions to the considered KdV-like equation, which are generated from polynomial solutions to the correspo...
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In this paper we establish the nonlinear stability of solitary travelling-wave solutions for the Kawahara-KdV equation ut + uux + uxxx − γ1uxxxxx = 0, and the modified Kawahara-KdV equation ut + 3u 2ux + uxxx − γ2uxxxxx = 0, where γi ∈ R is a positive number when i = 1, 2. The main approach used to determine the stability of solitary travelling-waves will be the theory developed by Albert in [1].
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By considering the set of coupled KdV differential equations as a zero curvature representation of some fourth order linear differential equation and factorizing the linear differential equation, the hierarchy of solutions of the coupled KdV differential equations have been obtained from the eigen spectrum of constant potentials.
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It is well known that provided scalar (1+1)-dimensional evolution equation possesses the infinitedimensional commutative Lie algebra of time-independent non-classical symmetries, it is either linearizable or integrable via inverse scattering transform [1, 2]. The standard way to prove the existence of such algebra is to construct the recursion operator [2]. But Fuchssteiner [3] suggested an alt...
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We introduce a new solution for Kawahara-KdV equations. The Lie group analysis is used to carry out the integration of this equations. The similarity reductions and exact solutions are obtained based on the optimal system method.
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1983
ISSN: 0386-2194
DOI: 10.3792/pjaa.59.407