Nonlocal Reductions of the Ablowitz-Ladik Equation

被引：15

作者：

Grahovski, G. G. ^{[1
]}

Mohammed, A. J. ^{[1
]}

Susanto, H. ^{[1
]}

机构：

[1] Univ Essex, Dept Math Sci, Colchester, Essex, England

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2018年 / 197卷 / 01期

关键词：

integrable system; soliton; PT symmetry; nonlocal reduction; Riemann-Hilbert problem; NONLINEAR SCHRODINGER-EQUATION; INVERSE SCATTERING TRANSFORM; SIMPLE LIE-ALGEBRAS; DIFFERENTIAL-DIFFERENCE EQUATIONS; NONVANISHING BOUNDARY-CONDITIONS; NON-HERMITIAN HAMILTONIANS; EVOLUTION-EQUATIONS; PSEUDO-HERMITICITY; SYMMETRIC-SPACES; SPECTRAL PROBLEM;

D O I：

10.1134/S0040577918100021

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Our purpose is to develop the inverse scattering transform for the nonlocal semidiscrete nonlinear Schrodinger equation (called the Ablowitz-Ladik equation) with symmetry. This includes the eigenfunctions (Jost solutions) of the associated Lax pair, the scattering data, and the fundamental analytic solutions. In addition, we study the spectral properties of the associated discrete Lax operator. Based on the formulated (additive) Riemann-Hilbert problem, we derive the one- and two-soliton solutions for the nonlocal Ablowitz-Ladik equation. Finally, we prove the completeness relation for the associated Jost solutions. Based on this, we derive the expansion formula over the complete set of Jost solutions. This allows interpreting the inverse scattering transform as a generalized Fourier transform.

引用

页码：1412 / 1429

页数：18

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