Abstract W.P. Duell

Justification of the Nonlinear Schrödinger approximation of the water wave problem and other quasilinear dispersive systems

Düll, Wolf-Patrick

Stuttgart University

Abstract: In order to describe the dynamics of oscillating wave packets in complicated dispersive evolutionary systems, the Nonlinear Schrödinger (NLS) equation can be formally derived as an approximation equation for the dynamics of the envelopes. To understand to which extent this approximation yield correct predictions of the qualitative behavior of the original systems it is important to justify the validity of the NLS approximation by estimates of the approximation errors in the physically relevant length and time scales. If the original systems are quasilinear, the justification of the NLS approximation is a highly nontrivial problem.

In this talk, we give an overview on the NLS approximation and its applications, for example, for modeling water waves, light pulses or spin waves, and discuss the strategy for proving the validity of the NLS approximation of quasilinear dispersive systems. Special emphasis will be put on the NLS approximation of the water wave problem.