We study the global existence and asymptotic behavior in time of solutions to the fourth order nonlinear Schrödinger type equation in one space dimension. The nonlinear interaction is the power type interaction with degree three, and it is a summation of a gauge invariant term and non-gauge-invariant terms. We prove the existence of modified wave operators for this equation with small final states. Here the modification of wave operator is only derived from the gauge invariant nonlinearity.
|Number of pages||20|
|Journal||Communications in Applied Analysis|
|Publication status||Published - Apr 1 2007|
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics