Construction, Lax integrability, bilinearization and multi-soliton solutions of a defocusing/focusing nonlocal extended modified Korteweg-de Vries equation

Abstract

Certain integrable nonlocal modified Korteweg-de Vries (mKdV)-type equations have been recently studied, which can be used on the atmospheric science and oceanic dynamics. In this study, a defocusing/focusing nonlocal extended mKdV equation is constructed via the Ablowitz-Kaup-Newell-Segur (AKNS) procedure. We also discuss the Lax integrability of that equation. By virtue of the improved Hirota bilinear method, some mutli-soliton solutions and bilinear forms are obtained. Profiles of certain multi-soliton solutions are shown graphically: (1) certain periodic solitons of that equation are shown; (2) certain quasi-periodic solitons of that equation are presented.