Geodesic
Positive periodic solutions for the Korteweg-de Vries equation
Electronic journal of differential equations, Tome 2007 (2007)
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 $u(0, x)\in {\dot B}^{\gamma}_{p, q}([a, b]), \gamma\notin \{1, 2, \dots\}, p greater than 1, q\geq 1, a less than b$ are fixed constants, $x\in [a, b]$. The period $\omega$ is arbitrary chosen and fixed.
Classification : 35Q53, 35Q35, 35G25
Keywords: nonlinear evolution equation, kortewg de Vries equation, periodic solutions 
@article{EJDE_2007__2007__a164,
     author = {Georgiev,  Svetlin Georgiev},
     title = {Positive periodic solutions for the {Korteweg-de} {Vries} equation},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1115.35110},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a164/}
}
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%A Georgiev,  Svetlin Georgiev
%T Positive periodic solutions for the Korteweg-de Vries equation
%J Electronic journal of differential equations
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Georgiev,  Svetlin Georgiev. Positive periodic solutions for the Korteweg-de Vries equation. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a164/