Geodesic
The existence of countably many stable cycles for a generalized cubic Schrödinger equation in a planar domain
Izvestiya. Mathematics, Tome 67 (2003) no. 6, pp. 1213-1242 
A. Yu. Kolesov; N. Kh. Rozov. The existence of countably many stable cycles for a generalized cubic Schrödinger equation in a planar domain. Izvestiya. Mathematics, Tome 67 (2003) no. 6, pp. 1213-1242. http://geodesic.mathdoc.fr/item/IM2_2003_67_6_a4/
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     author = {A. Yu. Kolesov and N. Kh. Rozov},
     title = {The existence of countably many stable cycles for a~generalized cubic {Schr\"odinger} equation in a~planar domain},
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     year = {2003},
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     url = {http://geodesic.mathdoc.fr/item/IM2_2003_67_6_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the boundary-value problem $$ u_t+i\Delta u=\varepsilon(u-d|u|^2u), \qquad u\big|_{\partial \Omega}=0, $$ in the domain $\Omega=\{(x,y)\colon 0\leqslant x\leqslant 1,0\leqslant y\leqslant 1\}$, where $u$ is a complex-valued function, $\Delta$ is the Laplace operators, $0\varepsilon\ll1$ and $d=1+ic_0$, $c_0\in\mathbb R$. We establish that it has countably many stable solutions that are periodic in $t$. We study the question of whether this phenomenon is preserved under a change of domain or boundary conditions.

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