The standard approach to integrable nonlinear evolution equations (NLEE) usually uses the
following steps:(1) Lax representation [L, M]= 0;(2) construction of fundamental analytic …

We consider the analytic vector breather and high-order rogue wave solutions for the
coupled nonlinear Schrödinger (NLS) equations with alternate signs of nonlinearities via …

Multi-component integrable generalizations of the Fokas–Lenells equation, associated with
each irreducible Hermitian symmetric space are formulated. Description of the underlying …

We start with a Riemann–Hilbert problem (RHP) related to BD. I-type symmetric spaces SO
(2 r+ 1)/S (O (2 r− 2 s+ 1)⊗ O (2 s)), s≥ 1. We consider two RHPs: the first is formulated on …

In the present paper we analyze the construction of fundamental analytic solutions (FAS) for
the generalized Kulish-Sklyanin models (KSM) for vanishing (VBC) and constant boundary …

Рассмотрена задача Римана–Гильберта, связанная с симметричными пространствами
SO (2r+ 1)/S (O (2r− 2s+ 1)⊗ O (2s)), s⩾ 1, типа BD. I. Речь идет о двух задачах Римана …

We consider a class of Lax operators L related to BD. I type symmetric spaces. They allow
one to solve special classes of vector NLS and matrix equations known as generalizations of …

We consider a class of Lax operators L related to BD. I type symmetric spaces. They allow
one to solve a special class of vector NLS equations which model Bose-Einstein …

Recently several new 2-component integrable NLS equations (2-NLSE) have been
discovered [1, 2]. Our main result is to demonstrate a family of 2-NLSE related to the …

The Manakov model [3] is the first example of a two-component Non-Linear Schrodinger
(NLS) equation that finds numerous applications in physics. It is natural to look for other …