Igor Rumanov: (2+1)-dimensional Whitham systems: 2dNLS, KP and others

Submitted by Jorge Cisneros on

Speaker: Igor Rumanov, University of Colorado Boulder

Date: May 19, 2022

Title: (2+1)-dimensional Whitham systems: 2dNLS, KP and others

Abstract: In this talk, the recently obtained Whitham modulation system for the (2+1)-dimensional nonlinear Schroedinger equation (2dNLS) will be described (joint work with Mark Ablowitz and Justin Cole). The first applications demonstrating its validity are the linear stability analysis of plane periodic traveling waves with its help and its KP-Whitham limit. The need for finding solutions of such systems raises a number of interesting questions. I will review the 2dNLS and KP Whitham systems in the context of the theory of previously known hydrodynamic integrable systems solvable by the generalized hodograph method. Understanding the 2dNLS Whitham system may be achieved by studying its multiple interesting reductions including the KP Whitham system. While the KP Whitham system is simpler and supposed to be integrable, finding its general solutions is still a challenge. The theory of hydrodynamic reductions may help as well as a better understanding of the well-known (1+1)-dimensional Whitham systems.