Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 49, pp. 1-13.

Title: Positive periodic solutions for the Korteweg-de Vries equation

Author: Svetlin Georgiev Georgiev (Univ. of Sofia, Bulgaria)

Abstract:
 In this paper we prove that the Korteweg-de Vries equation
 $$
 \partial_t u+\partial_x^3 u+u\partial_x u=0
 $$
 has unique positive solution $u(t, x)$ which is $\omega$-periodic
 with respect to the time variable $t$ and
 $u(0, x)\in {\dot B}^{\gamma}_{p, q}([a, b])$,
 $\gamma>0$, $\gamma\notin \{1, 2, \dots\}$, $p>1$, $q\geq 1$,
 $a<b$ are fixed constants, $x\in [a, b]$.
 The period $\omega>0$ is arbitrary chosen and fixed.
  
Submitted January 18, 2006. Published April 4, 2007.
Math Subject Classifications: 35Q53, 35Q35, 35G25
Key Words: Nonlinear evolution equation; Kortewg de Vries equation;
           periodic solutions.