Analysis Seminar

Integrable nonlocal nonlinear equations

Speaker: Ziad MUSSLIMANI, Florida State University

Location: Warren Weaver Hall 1302

Date: Thursday, November 7, 2019, 11 a.m.


A nonlocal nonlinear Schroedinger (NLS) equation was recently
introduced in Phys. Rev. Lett. 110, 064105 (2013) and shown to be an
integrable infinite dimensional Hamiltonian equation. Unlike the
classical (local) case, here the nonlinearly induced “potential” is
PT symmetric thus the nonlocal NLS equation is also PT symmetric. In
this talk, new reverse space-time and reverse time nonlocal nonlinear
integrable equations are discussed. They arise from remarkably simple
symmetry reductions of a general scattering problems where the
nonlocality appears in both space and time or time alone. They are
integrable infinite dimensional Hamiltonian dynamical systems. These
include the reverse space-time, and in some cases reverse time, nonlocal
NLS, modified KdV, sine-Gordon, multi-dimensional three-wave
interaction, derivative NLS, “loop soliton and Davey-Stewartson
equations. Lax pairs, an infinite number of conservation laws, inverse
scattering transforms are discussed and one soliton solutions are found.
Integrable reverse space-time and reverse time nonlocal discrete
nonlinear Schroedinger type equations are also introduced along with few
conserved quantities.