Geodesic
Positive periodic solutions for the Korteweg-de Vries equation
Electronic Journal of Differential Equations, Tome 2007 (2007).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Georgiev, Svetlin Georgiev},
     title = {Positive periodic solutions for the {Korteweg-de} {Vries} equation},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a164/}
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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/