Stability and instability results for standing waves of a quasilinear Schrodinger equations

Mathieu Colin (1, 2, 3, 4) , Louis Jeanjean (5) , Marco Squassina (6)

1 CARDAMOM - Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts
2 Bordeaux INP - Institut Polytechnique de Bordeaux
3 IMB - Institut de Mathématiques de Bordeaux
4 MC2 - Modélisation, contrôle et calcul
5 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
6 UNIVR | DI - Department of Computer Science [Verona]

We study a class of quasi-linear Schrödinger equations arising in the theory of superfluid film in plasma physics. 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.

Domaines: Equations aux dérivées partielles [math.AP]

Mathieu Colin, Louis Jeanjean, Marco Squassina. Stability and instability results for standing waves of a quasilinear Schrodinger equations. Nonlinearity, 2010, 23 (6), pp.1353-1385. ⟨10.1088/0951-7715/23/6/006⟩. ⟨hal-00547573⟩