Recent progress on nonlinear properties of parity-time (PT)-symmetric systems is
comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum …

A detailed survey of the technique of perturbation theory for nearly integrable systems,
based upon the inverse scattering transform, and a minute account of results obtained by …

In this Letter, we investigate an extended (3+ 1)-dimensional nonlinear Schrödinger
equation in an optical fiber. Via the truncated Laurent expansions, auto-Bäcklund …

Abstract In this paper, a (3+ 1)-dimensional Hirota-Satsuma-Ito-like equation is introduced
based on the (2+ 1)-dimensional Hirota-Satsuma-Ito equation. Bäcklund transformation and …

In this paper, we are concerned with the Riemann–Hilbert approach for the higher-order
Gerdjikov–Ivanov equation with nonzero boundary conditions. A uniformization variable will …

In the previous study, the one-lump solution is given to the dimensionally reduced forms of a
(3+ 1)-dimensional nonlinear model via the positive quadratic function method. The main …

The field of nonlinear dispersive waves has developed enormously since the work of Stokes,
Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s …

A systematic method is developed which allows one to identify certain important classes of
evolution equations which can be solved by the method of inverse scattering. The form of …

The general properties of the factorized S-matrix in two-dimensional space-time are
considered. The relation between the factorization property of the scattering theory and the …

A method is presented which enables one to obtain and solve certain classes of nonlinear
differential---< lifference equations. The introduction of a new discrete eigenvalue problem …