Chen Xiang-Jun

Conservation Laws for the Derivative Nonlinear Schrödinger Equation with Non-vanishing Boundary Conditions

Conservation laws for the derivative nonlinear Schrodinger equation with non-vanishing boundary conditions are derived, based on the recently developed inverse scattering transform using the affine parameter technique.

PERTURBED SPATIAL DARK SOLITONS

Effect of perturbations on spatial dark optical solitons is studied analytically with a novel direct perturbation approach for dark solitons. The problems of two-photon absorption and gain with saturation are reconsidered. The corresponding shifts of the soliton centers which have never been obtained by previous theories are given.

A SOLITON PERTURBATION THEORY FOR THE UNSTABLE NONLINEAR SCHR?DINGER EQUATION WITH CORRECTIONS

Based on the Zakharov-Shabat equation of the inverse scattering transform for the unstable nonlinear Schr?dinger equation, for which a perturbation theory with corrections is developed in this paper. All necessary formulae for calculating the scattering data are derived. Based upon these formulae, the effect due to the corrections can be studied. As an example, the correction due to the damping is calculated.

Spherical-Harmonic Expansion Solution of Classical Transport Equations of Quark

The spherical-harmonic method of solving classical transport equation of quark is investigated. The hydrodynamics description of QGP as well as the relation between diffusion approximation and collective flow in nuclear collisions are discussed.

Explicit N-Solit on Solution of the Unstable Nonlinear Schrödinger Equation

The unstable nonlinear Schrodinger (NLS) equation is solved by the inverse scattering transform. Based on the constructed Zakharov–Shabat equation, it is shown that the soliton solution of the unstable NLS equation can be known from the soliton solution of the usual NLS equation by simply exchanging the tariables. The explicit N-soliton solution and the position shifts due to the collision are thus calculated.