Stability of solitary waves for the vector nonlinear Schrodinger equation in higher-order Sobolev spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:409

Article

Nguyen, Nghiem V.

关键词: Ground states;    Solitary waves;    Orbital stability;    Nonlinear Schrodinger system;   

DOI  :  10.1016/j.jmaa.2013.07.050

来源: Elsevier

【 摘 要 】

In this manuscript, a sharp form of orbital stability for the Schrodinger system, also known as the vector NLS, i partial derivative/partial derivative tu(j) + partial derivative(2)/partial derivative xxu(j) + 2 Sigma(m)(i=1)vertical bar u(i)vertical bar(2)u(j) = 0, where u(j) are complex-valued functions of (x, t) is an element of R-2, j = 1, 2, ..., m, is established in L-2-based Sobolev classes of arbitrarily high order. The result means practically that not only does the bulk of what emanates from the perturbed solitary wave stay close in shape and propagation and phase speeds to the original solitary wave, but emerging residual oscillations must also be very small and not only in the energy norm. Published by Elsevier Inc.

【 授权许可】

Free