Positive periodic solutions for the Korteweg-de Vries equation

Electronic Journal of Differential Equations

关键词: Nonlinear evolution equation;    Kortewg de Vries equation;    periodic solutions.;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this paper we prove that the Korteweg-de Vries equation $$ partial_t u+partial_x^3 u+upartial_x u=0 $$ has unique positive solution $u(t, x)$ which is $omega$-periodic with respect to the time variable $t$ and $u(0, x)in {dot B}^{gamma}_{p, q}([a, b])$, $gamma>0$, $gamma otin {1, 2, dots}$, $p>1$, $qgeq 1$, $a0$ is arbitrary chosen and fixed.

【 授权许可】

Unknown