Exploring the dynamic behaviors of the damping nonlinear Schrödinger equation (NLSE)
with periodic perturbation is a challenge in the field of nonlinear science, because the …

Taking the nonlinear Schrödinger equation (NLSE) as an example, we provide from a
mathematical viewpoint, rigorous evidence that numerical noise of a chaotic system as tiny …

In this paper we study the non-equilibrium dynamics of one-dimensional Bose gas from the
general perspective of the dynamics of integrable systems. After outlining and critically …

We construct explicit forms for two non-trivial conservation laws of the quantum non-linear
Schrödinger equation and show that they have the correct quasi-classical limit. For H 4 the …

The one-dimensional problem of N particles with contact interaction in the presence of a
tunable transmitting and reflecting impurity is investigated along the lines of the coordinate …

The spread of the wave-function, or quantum uncertainty, is a key notion in quantum
mechanics. At leading order, it is characterized by the quadratic moments of the position and …

A bstract The effect of unstable quasiparticles in the out-of-equilibrium dynamics of certain
integrable systems has been the subject of several recent studies. In this paper we focus on …

Quantum non-linear SCHROEDINGER equation is equivalent to Lieb-Liniger model. It has
non-trivial conservation laws. Recently these conservation laws were used for evaluation of …

We establish the exact solution of the nonlinear Schrödinger equation with a delta-function
impurity, representing a pointlike defect which reflects and transmits. We solve the problem …

We propose an exactly solvable model of one-dimensional anyons with competing δ-
function and derivative δ-function interaction potentials. The Bethe ansatz equations are …