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

We study a class of quasi-linear Schrodinger 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 orbit...

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Bibliographic Details
Published in:Nonlinearity 2010-06, Vol.23 (6), p.1353-1385
Main Authors: Colin, Mathieu, Jeanjean, Louis, Squassina, Marco
Format: Article
Language:English
Subjects:
Calculus of variations and optimal control
Cauchy problem
Derivation
Exact sciences and technology
Fluids
Global analysis, analysis on manifolds
Instability
Mathematical analysis
Mathematical methods in physics
Mathematics
Other topics in mathematical methods in physics
Partial differential equations
Physics
Regularity
Schroedinger equation
Sciences and techniques of general use
Stability
Standing waves
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Variational methods
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Summary:We study a class of quasi-linear Schrodinger 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.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/23/6/006