# 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.

**Synopsis:**

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.