Stability and instability results for standing waves of quasi-linear Schrödinger equations

Details Stability and instability results for standing waves of quasi-linear Schrödinger equations Stability and instability results for standing waves of quasi-linear Schrödinger equations

2009-06-29

arxiv.org/abs/0906.5261v2

Mathematics

Analysis of PDEs

40 pages

Scientific paper

We study a class of quasi-linear Schr\"odinger equations arising in the theory of superfluid film in plasma physics. First, using gauge transforms and a derivation process we solve, under some regularity assumptions, the Cauchy problem. Then, by means of variational methods, we study the existence, the orbital stability and instability of standing waves which minimize some associated energy.

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