Orbital stability of periodic traveling-wave solutions for the regularized Schamel equation
نویسندگان
چکیده
منابع مشابه
The stability analysis of the periodic traveling wave solutions of the mKdV equation
The stability of periodic solutions of partial differential equations has been an area of increasing interest in the last decade. In this paper, we derive all periodic traveling wave solutions of the focusing and defocusing mKdV equations. We show that in the defocusing case all such solutions are orbitally stable with respect to subharmonic perturbations: perturbations that are periodic with p...
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In this paper, we study the orbital stability for a four-parameter family of periodic stationary traveling wave solutions to the generalized Korteweg-de Vries (gKdV) equation ut = uxxx + f(u)x. In particular, we derive sufficient conditions for such a solution to be orbitally stable in terms of the Hessian of the classical action of the corresponding traveling wave ordinary differential equatio...
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Article history: Received 21 December 2013 Received in revised form 19 April 2014 Accepted 23 April 2014 Available online 14 May 2014 Communicated by C.R. Doering
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The nonlinear Schrödinger equation has several families of quasi-periodic travelling waves, each of which can be parametrized up to symmetries by two real numbers: the period of the modulus of the wave profile, and the variation of its phase over a period (Floquet exponent). In the defocusing case, we show that these travelling waves are orbitally stable within the class of solutions having the...
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Solitons are ubiquitous and exist in almost every area from sky to bottom. For solitons to appear, the relevant equation of motion must be nonlinear. In the present study, we deal with the Korteweg-deVries (KdV), Modied Korteweg-de Vries (mKdV) and Regularised LongWave (RLW) equations using Homotopy Perturbation method (HPM). The algorithm makes use of the HPM to determine the initial expansion...
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ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 2016
ISSN: 0167-2789
DOI: 10.1016/j.physd.2015.12.002