Evgeny Lakshtanov, Boris Vainberg
Published 2018-03-02Version 1
We consider the two dimensional focusing Davey-Stewartson II system and construct the global solution of the Cauchy problem for a dense in $L^2(\mathbb C)$ set of initial data. We do not assume that the initial data is small. So, the solutions may have singularities. We show that the blow-up may occur only on a real analytic variety and the variety is bounded in each strip $t \leq T$.
KdV equation beyond standard assumptions on initial data
On the Cauchy problem for a higher-order $μ$-Camassa-Holm equation
A global solution to the Schrödinger equation: from Henstock to Feynman
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