RiemannHilbert problem for the focusing nonlinear Schrödinger equation with multiple highorder poles under nonzero boundary conditions
Abstract
The RiemannHilbert (RH) problem is developed to study the focusing nonlinear Schrödinger (NLS) equation with multiple highorder poles under nonzero boundary conditions. Laurent expansion and Taylor series are employed to replace the residues at the simple and the secondpoles. Furthermore, the solution of RH problem is transformed into a closed system of algebraic equations, and the soliton solutions corresponding to the transmission coefficient 1 /s_{11}(z) with an Norder pole are obtained by solving the algebraic system. Then, in a more general case, the transmission coefficient with multiple highorder poles is studied, and the corresponding solutions are obtained. In addition, for highorder pole, the propagation behavior of the soliton solution corresponding to a thirdorder pole and the mixed case of a secondorder pole and a simple pole are given as example.
 Publication:

Physica D Nonlinear Phenomena
 Pub Date:
 April 2022
 DOI:
 10.1016/j.physd.2022.133162
 arXiv:
 arXiv:2104.00966
 Bibcode:
 2022PhyD..43233162Y
 Keywords:

 The focusing nonlinear Schrödinger equation;
 RiemannHilbert problem;
 Multiple highorder poles;
 Nonzero boundary conditions;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematical Physics
 EPrint:
 19 pages, 5 figures