3 research outputs found

    On finite energy solutions of the KP-I equation

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    We prove that the flow map of the Kadomtsev-Petviashvili-I (KP-I) equation is not uniformly continuous on bounded sets of the natural energy space.Comment: 14 page

    Discrete rogue waves and blow-up from solitons of a nonisospectral semi-discrete nonlinear Schr\"{o}dinger equation

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    We investigate the nonisospectral effects of a semi-discrete nonlinear Schr\"{o}dinger equation, which is a direct integrable discretisation of its continuous counterpart. Bilinear form and double casoratian solution of the equation are presented. Dynamics of solutions are analyzed. Both solitons and multiple pole solutions admit space-time localized rogue wave behavior. And more interestingly, the solutions allow blow-up at finite time tt.Comment: 10 pages, 9 figure

    Rational solutions to the ABS list: Degenerating approach

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    In the paper we first construct rational solutions for the Nijhoff-Quispel-Capel (NQC) equation by means of bilinear method. These solutions can be transferred to those of Q3δ_\delta equation in the Adler-Bobenko-Suris (ABS) list. Then making use of degeneration relation we obtain rational solutions for Q2, Q1δ_\delta, H3δ_\delta, H2 and H1. These rational solutions are in Casoratian form and the basic column vector satisfies an extended condition equation set.Comment: 19 pages,Typos correcte
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