Nonlocal Complex Modified Korteweg-de Vries Equations: Reductions and Exact Solutions

Abstract

We present three different two-dimensional nonlocal integrable cmKdV equations obtained by Ablowitz-Musslimani type of reductions which are respectively T-symmetric, S-symmetric, and ST-symmetric nonlocal cmKdV equations. Ablowiz - Musslimani type of reduction arises from remarkably simple symmetry reductions of general AKNS scattering problems where the nonlocality appears in both space and time or time alone. Moreover, we obtain exact solutions by Darboux transformation.