一类非线性Schrödinger-KdV微扰系统的初值问题

Korteweg-de Vries(KdV)方程是一种数学模型,用于描述色散介质中长波的传播.而非线性薛定谔(NLS)方程模拟了由短色散波组成的窄带宽波包的动态,它是描述许多物理系统的有用模型,包括玻色-爱因斯坦凝聚、光纤和水波等.将KdV和NLS方程耦合起来的系统可以模拟长波和短波的相互作用.这个系统在物理和数学上很有吸引力,它结合了两个模型的优点.KdV方程描述的长波可以影响NLS方程描述的短波的行为,而短波反过来也可以影响长波的行为.

Analytic Solutions to Forced KdV Equation

The Korteweg-de Vries equation with a forcing term is established by recent studies as a simple mathematicalmodel of describing the physics of a shallow layer of fluid subject to external forcing.In the present paper,we study theanalytic solutions to the KdV equation with forcing term by using Hirota's direct method.Several exact solutions aregiven as examples,from which one can see that the same type soliton solutions can be excited by different forced term.

Rogue Wave, Breathers and Bright-Dark-Rogue Solutions for the Coupled Schrodinger Equations

We construct explicit rogue wave solutions,breather solitons,and rogue-bright-dark solutions for the coupled non-linear Schrodinger equations by the Darboux transformation.

Global attractor for Hirota equation

The long time behavior of solution for Hirota equation with zero order dissipation is studied. The global weak attractor for this system in Hper^k is constructed. And then by exact analysis of the energy equation, it is shown that the global weak attractor is actually the global strong attractor in Hper^k.

Orbital Stability of Solitary Waves for Generalized Zakharov System

In the interaction of laser-plasma the system of Zakharov equation plays an important role.This system attracted many scientists' wide interest and attention.And the formation, evolution and interaction of the Langmuir solutions differ from solutions of the KDV equation. Here we consider the following generalized Zakharov

Blow-up Solutions to a Viscoelastic Fluid System and a Coupled Navier–Stokes/Phase-Field System in R^(2)

The explicit solutions to both the Oldroyd-B model with an infinite Weissenberg number and the coupled Navier–Stokes/phase-field system are constructed by the method of separation of variables.It is found that the solutions blow up in finite time.

The Existence of Global Attractor for Zakharov Equations Arising from Ion-acoustic Modes

在这份报纸，我们为从离子声学的模式产生的 Zakharov 方程考虑起始边界的问题并且获得全球引起注意的人的存在为起始 -- 为 Zakharov 方程的边界问题。