We study two members of the multi-component AKNS hierarchy. These are multi-NLS and multi-MKdV systems. derive Hirota bilinear forms these equations obtain soliton solutions. find all possible local nonlocal reductions systems give a prescription to their also (2+1)-dimensional extensions

In our papers [20, 21] we proposed a new approach to integrable hierarchies of soliton equations and their quantum deformations. We have applied this approach to the Toda field theories and the generalized KdV and modified KdV (mKdV) hierarchies. In this paper we apply our approach to the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy [1] and its generalizations. In particular, we show that the fr...

A compact expression for the generating function of the constants of motion for the nonlinear Schrödinger equation is derived using the functional representation of the AKNS hierarchy.

In our papers [20, 21] we proposed a new approach to integrable hierarchies of soliton equations and their quantum deformations. We have applied this approach to the Toda field theories and the generalized KdV and modified KdV (mKdV) hierarchies. In this paper we apply our approach to the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy [1] and its generalizations. In particular, we show that the fr...

We develop a formalism of multicomponent BKP hierarchies using elementary geometry of spinors. The multicomponent KP and the modified KP hierarchy (hence all their reductions like KdV, NLS, AKNS or DS) are reductions of the multicomponent BKP.

The purpose of this paper is to construct a generalized r-matrix structure of finite dimensional systems and an approach to obtain the algebro-geometric solutions of integrable nonlinear evolution equations (NLEEs). Our starting point is a generalized Lax matrix instead of usual Lax pair. The generalized r-matrix structure and Hamiltonian functions are presented on the basis of fundamental Pois...

Zakharov-Shabat–Ablowitz-Kaup-Newel-Segur (ZS–AKNS) representation for Stokes-anti-Stokes stimulated Raman scattering (SRS) is proposed. Periodical waves, solitons and self-similarity solutions are derived. Transient and bright threshold solitons are discussed. December 29, 1994 Sofia

By using disipative version of the second and the third members of AKNS hierarchy, a new method to solve 2+1 dimensional KadomtsevPetviashvili (KP-II) equation is proposed. We show that dissipative solitons (dissipatons) of those members give rise to the real solitons of KP-II. From the Hirota bilinear form of the SL(2,R) AKNS flows, we formulate a new bilinear representation for KP-II, by whic...