Semi-Analytical Solutions of Time-Fractional KdV and Modified KdV Equations
نویسندگان
چکیده
منابع مشابه
Nonlinear Stability of Solitary Travelling-wave Solutions for the Kawahara-kdv and Modified Kawahara-kdv Equations
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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The initial value problems for the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations under periodic and decaying boundary conditions are considered. These initial value problems are shown to be globally well-posed in all L 2-based Sobolev spaces H s where local well-posedness is presently known, apart from the H 1 4 (R) endpoint for mKdV. The result for KdV relies on a new method for co...
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ژورنال
عنوان ژورنال: Scientific Inquiry and Review
سال: 2019
ISSN: 2521-2435,2521-2427
DOI: 10.32350/sir.34.04