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Strong instability of standing waves for a system NLS with quadratic interaction

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arxiv 1810.00676 v1 pith:RSXU5UUM submitted 2018-09-28 math.AP

Van Duong Dinh This is my paper · ORCID
classification math.AP
keywords instabilityinteractionquadraticstandingstrongsystemwavescondition
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abstract

We study the strong instability of standing waves for a system of nonlinear Schr\"odinger equations with quadratic interaction under the mass resonance condition in dimension $d=5$.

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  1. On a system of Schr\"odinger equations with general quadratic-type nonlinearities

    math.AP 2019-08 accept novelty 6.0 of 10

    For a broad class of quadratic-type Schrödinger systems in dimensions 1 through 6, the paper proves that ground states of the elliptic system govern the global-existence/blow-up dichotomy and the stability of standing waves.

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