Symmetry reductions for a dissipation-modified KdV equation
نویسندگان
چکیده
منابع مشابه
Nonclassical Symmetry Reductions for Coupled KdV Equations
In this paper, by using the nonclassical method, several new symmetries and solutions are obtained, which are unobtainable by Lie classical symmetries.
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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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The Cauchy problem for the modified KdV-equation ut + uxxx = (u 3)x, u(0) = u0 is shown to be locally wellposed for data u0 in the space Ĥr s (R) defined by the norm ‖u0‖ Ĥr s := ‖〈ξ〉sû0‖Lr′ ξ , provided 4 3 < r ≤ 2, s ≥ 1 2 − 1 2r . For r = 2 this coincides with the best possible result on the H-scale due to Kenig, Ponce and Vega. The proof uses an appropriate variant of the Fourier restrictio...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2003
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(03)80025-3