The nonlinear Fourier transform, which is also known as the forward scattering transform,
decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common …

We show that the Ablowitz-Ladik equation, which is an integrable form of the discretized
nonlinear Schrödinger equation, has rogue wave solutions in the form of the rational …

Based on the stationary zero-curvature equation and the Lenard recursion equations, we
derive the coupled modified Korteweg–de Vries (cmKdV) hierarchy associated with a 3× 3 …

The theory of tetragonal curves is established and first applied to the study of algebro-
geometric quasi-periodic solutions of discrete soliton equations. Using the zero-curvature …

The aim of this work is multifold. Firstly, it intends to present a complete, quantitative and self-
contained description of the periodic traveling wave solutions and Whitham modulation …

Abstract To decompose the (2+ 1)-dimensional Gardner equation, an isospectral problem
and a corresponding hierarchy of (1+ 1)-dimensional soliton equations are proposed. The …

The nonlinearization approach of Lax pairs is extended to the discrete Ablowitz–Ladik
hierarchy. A new symplectic map and a class of new finite‐dimensional Hamiltonian systems …

In this paper, we consider the robust inverse scattering method for the Ablowitz–Ladik (AL)
equation on the non-vanishing background, which can be used to deal with arbitrary-order …

This is a continuation of a study on Riemann theta function representations of algebro-
geometric solutions to soliton hierarchies. In this part, we straighten out all flows in soliton …

Based on solving the Lenard recursion equations and the zero-curvature equation, we
derive the Kaup–Kupershmidt hierarchy associated with a 3× 3 matrix spectral problem …