Global solution of the initial value problem for the focusing Davey-Stewartson II system

Abstract

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 $t\le T$.

References in corpus (2)

• Approximating with Gaussians
• Soliton Solutions and their (In)stability for the Focusing Davey-Stewartson II Equation

Cited by in corpus (1)

• Recovery of $L^p$-potential in the plane