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

Abstract

We give a rigorous mathematical analysis of the one-soliton solution of the focusing Davey-Stewartson II equation and a proof of its instability under perturbation. Building on the fundamental perturbation analysis of Gadyl'shin and Kiselev, we verify their Assumption 1 and use Fredholm determinants to globalize their perturbation analysis.

32 pages, 1 figure

Cited by in corpus (2)

• Global solution of the initial value problem for the focusing Davey-Stewartson II system
• Numerical study of blow-up mechanisms for Davey-Stewartson II systems