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.
Colin, M., Jeanjean, L., Squassina, M., Stability and instability results for standing waves of quasi-linear Schrodinger equations, <<NONLINEARITY>>, 2010; 23 (6): 1353-1385. [doi:10.1088/0951-7715/23/6/006] [http://hdl.handle.net/10807/89959]
Stability and instability results for standing waves of quasi-linear Schrodinger equations
Squassina, MarcoUltimo
2010
Abstract
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.
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