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Non-localized standing waves of the hyperbolic cubic nonlinear Schrödinger equation

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  • We construct two families of non-localized standing waves for the hyperbolic cubic nonlinear Schrödinger equation \[iu_t+u_{xx}-u_{yy}+|u|^2u=0.\] The first family of standing waves consists of solutions which correspond to some generalized breathers for each fixed time $t$, while solutions in the second family are periodic both in $x$ and $y$. The second family of solutions were numerically observed by Vuillon, Dutykh and Fedele in a recent preprint [17].
    Mathematics Subject Classification: Primary: 37C27, 37C29; Secondary: 35B25, 35B36.


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