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Long-Time Asymptotics for the Nonlocal MKdV Equation

He, Feng-Jing ; Fan, En-Gui ; Xu, Jian

Communications in theoretical physics, 2019-05, Vol.71 (5), p.475 [Periódico revisado por pares]

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Título:
Long-Time Asymptotics for the Nonlocal MKdV Equation
Autor: He, Feng-Jing ; Fan, En-Gui ; Xu, Jian
É parte de: Communications in theoretical physics, 2019-05, Vol.71 (5), p.475
Descrição: Abstract In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation (nonlocal mKdV) q t (x, t) + q xxx (x,t) −6q(x, t)q(−x, −t)q x (x, t) = 0, which can be viewed as a generalization of the local classical mKdV equation. We first formulate the Riemann-Hilbert problem associated with the Cauchy problem of the nonlocal mKdV equation. Then we apply the Deift-Zhou nonlinear steepest-descent method to analyze the long-time asymptotics for the solution of the nonlocal mKdV equation. In contrast with the classical mKdV equation, we find some new and different results on long-time asymptotics for the nonlocal mKdV equation and some additional assumptions about the scattering data are made in our main results .
Idioma: Inglês

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