3 research outputs found
On finite energy solutions of the KP-I equation
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
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 .Comment: 10 pages, 9 figure
Rational solutions to the ABS list: Degenerating approach
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 Q3 equation in the
Adler-Bobenko-Suris (ABS) list. Then making use of degeneration relation we
obtain rational solutions for Q2, Q1, H3, 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