Existence, stability of standing waves and the characterization of finite time blow-up solutions for a system NLS with quadratic interaction

Van Duong Dinh

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arXiv · 1809.09643

Existence, stability of standing waves and the characterization of finite time blow-up solutions for a system NLS with quadratic interaction

Van Duong Dinh

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Abstract

We study the existence and stability of standing waves for a system of nonlinear Schr\"odinger equations with quadratic interaction in dimensions $d\leq 3$. We also study the characterization of finite time blow-up solutions with minimal mass to the system under mass resonance condition in dimension $d=4$. Finite time blow-up solutions with minimal mass are showed to be (up to symmetries) pseudo-conformal transformations of a ground state standing wave.

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Van Duong Dinh. 2018-09-25. Existence, stability of standing waves and the characterization of finite time blow-up solutions for a system NLS with quadratic interaction. https://arxiv.org/abs/1809.09643

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