Seminar 31/03/17: Integrable nonlocal multi-component equations with PT and CPT symmetries

Integrable nonlocal multi-component equations with PT and CPT symmetries
Georgi Grahovski
University of Essex
Friday 31 March 2017
2.30pm, Room KE2-008, 2nd Floor, Main Building, DIT Kevin Street

Abstract:

We will present extensions of N-wave and derivative NLS types of equations with PT and CPT-symmetries. The types of (nonlocal) reductions leading to integrable equations invariant with respect to C- (charge conjugation), P- (spatial reflection) and T- (time reversal) symmetries are described. The corresponding constraints on the fundamental analytic solutions and the scattering data are derived.

Based on examples of 3-wave (related to the algebra sl(3,C)) and 4-wave (related to the algebra so(5,C)) systems, the properties of different types of 1- and 2-soliton solutions are discussed. It is shown that the PT symmetric 3-wave equations may have regular multi-soliton solutions for some specific choices of their parameters. Furthermore, we will present multi-component generalizations of derivative nonlinear Schrodinger (DNLS) type of related to A.III symmetric spaces and having with CPT-symmetry. This includes equations of Kaup-Newell (KN) and Gerdjikov-Ivanov (GI) types.