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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

QUINTERO, José R.. Stability and instability analysis for the standing waves for a generalized Zakharov-Rubenchik system. Proyecciones (Antofagasta) [online]. 2022, vol.41, n.3, pp.663-682. ISSN 0716-0917.  http://dx.doi.org/10.22199/issn.0717-6279-4547.

In this paper, we analyze the stability and instability of standing waves for a generalized Zakharov-Rubenchik system (or the Benney-Roskes system) in spatial dimensions N = 2, 3. We show that the standing waves generated by the set of minimizers for the associated variational problem are stable, for N = 2 and σ(p − 2) > 0. We also show that the standing waves are strongly unstable, for N = 3 and if either σ < 0 and 4/3 <p< 4, or σ > 0 and 0 <p< 2. Results follow by using the variational characterization of standing waves, the concentration compactness principle due to J. Lions and the compactness lemma due to E. Lieb to solve the associated minimization problem.

Keywords : standing waves; virial identity; stability; blow up.

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