广义Davey-Stewartson方程的孤波解

在本文中,利用辅助的常微分方程来代替更一般的方程,扩张映射方法被呈现.通过这种方法,使用符号计算关于Davey-Stewartson方程的许多新的孤波解被构造.     

The Hirota Method and Soliton Solutions to the Multidimensional Nonlinear Schrodinger Equation

Using the Hirota method, we obtain a 1-soliton solution to the (3+1)-dimensional nonlinear Schrodinger equation.     

广义Pochhammer-Chree方程的新孤波解和余弦周期波解

本文利用假设待定法求出了具5阶非线性项的广义Pochhammer-Chree方程具双曲正割函数分式形式的2个新孤波解和6个余弦函数周期波解,并分别给出了它们的有界性条件.揭示了行波波速v的改变与钟状孤波解和余弦周期波解波形变化的相关性.     

Soliton Solutions for a Generalized Quasilinear Elliptic Problem

Potential Analysis - We establish existence and multiplicity of solutions for the elliptic quasilinear Schrödinger equation $$ -\text{div}(g^{2}(u)\nabla u) +g(u)g^{\prime}(u)|\nabla u|^{2}+...     

广义耦合KdV孤子方程的达布变换及其奇孤子解

借助谱问题的规范变换, 给出广义耦合KdV孤子方程的达布变换,利用达布变换来产生广义耦合KdV孤子方程的奇孤子解,并且用行列式的形式来表达广义耦合KdV孤子方程的奇孤子解．作为应用,广义耦合KdV孤子方程奇孤子解的前两个例子被给出．     

广义耦合KdV孤子方程的达布变换及其偶孤子解

根据广义耦合KdV孤子方程的Lax对, 借助谱问题的规范变换, 一个包含多参数的达布变换被构造出来. 利用达布变换来产生广义耦合KdV孤子方程的偶孤子解, 并且用行列式的形式来表达广义耦合KdV孤子方程的偶孤子解. 作为应用, 广义耦合KdV孤子方程的偶孤子解的前两个例子被给出.     

广义KdV方程与广义Burgers方程的精确解

利用试探函数法和直接积分法构造广义KdV方程与广义Burgers方程的新的精确解.     

The Properties of Solutions for a Generalized b-Family Equation with Peakons

This paper deals with the Cauchy problem for a shallow water equation with high-order nonlinearities, y _t +u ^m+1 y _x +bu ^m u _x y=0, where b is a constant, $m\in \mathbb{N}$ , and we have the notation $y:= (1-\partial_{x}^{2}) u$ , which includes the famous Camassa–Holm equation, the Degasperis–Procesi equation, and the Novikov equation as special cases. The local well-posedness of strong solutions for the equation in each of the Sobolev spaces $H^{s}(\mathbb{R})$ with $s>\frac{3}{2}$ is obtained, and persistence properties of the strong solutions are studied. Furthermore, although the $H^{1}(\mathbb{R})$ -norm of the solution to the nonlinear model does not remain constant, the existence of its weak solutions in each of the low order Sobolev spaces $H^{s}(\mathbb{R})$ with $1<s<\frac{3}{2}$ is established, under the assumption $u_{0}(x)\in H^{s}(\mathbb{R})\cap W^{1,\infty}(\mathbb{R})$ . Finally, the global weak solution and peakon solution for the equation are also given.     

带非齐次项和Sobolev Hardy临界指数的奇异椭圆方程的多解

该文讨论一个带非齐次项和Sobolev Hardy临界指数的半线性奇异椭圆型方程的多解问题. 证明了当方程中的参数小于某个已知的常数时，所考虑的问题有两个解     

一类广义Burgers-Huxley方程的解与其分支

运用平面动力系统分支理论和可积性判定方法,研究了一类广义Burgers-Huxley方程,首先通过新的算法计算奇点量,解决了其可积性问题,然后进行平衡点类型分析,并讨论了在不同的参数条件下的相图与分支类型,利用Maple软件绘出分支相图,最后讨论了各种行波解的存在性及方程的精确解.     

一个广义非线性扰动Klein-Gordon方程孤子解

研究了一个广义非线性扰动Klein-Gordon方程.利用同伦映射方法,首先构造了相应的同伦映射;然后选取了适当的初始近似;并计算各阶相应孤子近似解.同时还考虑了一个微扰方程.     

Similarity Solutions of a Generalized Burgers Equation

The similarity method is applied to a generalized Burgers equationwhich has been applied to shock waves and to sound waves. Threedifferent cases of the equation, each allowing a three-parametersymmetry group, are found. The corresponding reduction to anordinary differential equation is given. The Lie algebras ofthe groups are identified with standard types given by Bianchi.     

Solitary Wave Solutions and Kink Wave Solutions for a Generalized PC Equation

We present in this paper a generalised PC (GPC) equation which includes several known models. The corresponding traveling wave system is derived and we show that the homoclinic orbits of the traveling wave system correspond to the solitary waves of GPC equation, and the heteroclnic orbits correspond to the kink waves. Under some parameter conditions, the existence of above two types of orbits is demonstrated and the explicit expressions of the two solutions are worked out.     

Travelling Wave Solutions for Generalized Fisher Equation

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Solutions of the Camassa-Holm Equation Near the Soliton

In this paper, solutions of the Camassa-Holm equation near the soliton Q is decomposed by pseudoconformal transformation as follows: λ^1/2(t)u(t, λ(t)y + x(t)) = Q(y) + ε(t, y), and the estimation formula with respect to ε(t, y) is obtained: |ε(t, y)| ≤ Ca₃Te^-θ|y|+ |λ^1/2(t)ε₀|. For the CH equation, we prove that the solution of the Cauchy problem and the soliton Q is sufficiently close as y → ∞, and the approximation degree of the solution an...     

含临界位势的广义平均曲率方程的解

讨论一个含临界位势的广义平均曲率方程在Dirichlet边界条件下解的存在性.此方程相应的变分泛函关于u的梯度非齐次,且Sobolev空间嵌入失去紧性.为了克服这些困难,本文将关于范数的一个基本结论推广到一般的偶泛函,并利用C.K.N不等式及Ambrosetti的山路引理证明了方程存在非平凡解.     

Stationary Solutions for a Generalized Kadomtsev-Petviashvili Equation in Bounded Domain

In this work, we are mainly concerned with the existence of stationary solutions for a generalized Kadomtsev-Petviashvili equation in bounded domain of Rn. We utilize variational method and critical point theory to establish our main results.     

一类广义Boussinesq方程的Wronskian行列式解

为了构造非线性孤子方程的Wronskian行列式新解,进一步研究了Wronskian技巧.本文首先给出非线性广义Boussinesq方程的双线性形式,利用Wronskian技巧构造出该非线性方程所满足的一个线性偏微分条件方程组,然后求解该微分条件方程组,得到了广义Boussinesq方程的各种Wronskian行列式解.     

Sensitivity of Solutions to a Parametric Generalized Equation

In the present paper we prove that, under some suitable conditions on multifunctions $C\!: {I\!\!R}^l\rightrightarrows {I\!\!R}^n$ , $F\!:{I\!\!R}^d\times {I\!\!R}^n\rightrightarrows {I\!\!R}^m$ , and $K\!:{I\!\!R}^l\times {I\!\!R}^n\rightrightarrows {I\!\!R}^m$ , the generalized perturbation multifunction $G\!: {I\!\!R}^d\times{I\!\!R}^l\times {I\!\!R}^m\rightrightarrows {I\!\!R}^n$ , of the form $$G(\mu,\lambda,\nu)=\{x\in C(\lambda)\ |\ \nu\in F(\mu,x)+K(\lambda,x)\},$$ is proto-differentiable at (μ, λ, ν) relative to x?∈?G(μ, λ, ν). Moreover, in a special case, where K(λ, x) is a normal cone to C(λ) at x, we also provide sufficient conditions for G(·) to be single-valued on a neighborhood of (μ, λ, ν) and semi-differentiable at (μ, λ, ν).