The simplest oscillating solutions of nonlocal nonlinear models

Abstract

In their recent works, Ablowitz and Musslimani proposed a new type of integrable nonlinear equations – nonlocal analogues of the nonlinear Schrödinger equation, the modified Korteweg-de Vries equation, and other nonlinear differential equations. In subsequent works, numerous researchers constructed the simplest soliton and rational solutions of these equations. In this paper, we construct the simplest oscillating solutions of some of the integrable nonlocal nonlinear differential equations associated to the nonlinear Schrödinger equation.

Finite-gap solutions of nonlocal equations in Ablowitz-Kaup-Newell-Segur hierarchy

“…We considered single-phase solutions of nonlocal equations in AKNS hierarchy in works [31]- [33]. This is why in what follows we assume that > 1.…”

“…Then there arose a natural question on the possibility of constructing solutions of nonlocal integrable equations by the method of finite-zone integration. Our first results on the theory of finite-zone solutions of nonlocal integrable equations from the AKNS hierarchy were published in papers [31]- [33]. In this paper, we summarize our research on this topic.…”