广义射影Riccati方程方法与(2+1)维色散长波方程新的精确行波解

助于符号计算软件Maple,通过一种构造非线性偏微分方程更一般形式行波解的直接方 法,即改进的广义射影Ricccati方程方法,求解(2 1)维色散长波方程,得到该方程的新的 更一般形式的行波解,包括扭状孤波解,钟状解,孤子解和周期解．并对部分新形式孤波解画 图示意．     

磁绝缘传输线振荡器中辐射场的非线性行为

 导出了磁绝缘传输线振荡器(MILO)中辐射场的非线性演化方程，并讨论了在临界值点附近可能出现非线性不稳定解的条件。结论是：(1)非线性增长速率与线性增长速率的比值g<1.2，且远离g+γ=1(γ为非线性相位增长率与线性相位增长率的比值)点时，出现非稳定解的失谐量临界值很小，而线性增长速率临界值临界值很大，容易出现非稳定解；(2)当g≥1.2时，任意小的失谐量都可以使场出现非稳定解；(3)线性增长速率越大，越不容易出现非稳定解。     

求解第一类Fredholm积分方程的一种新的正则化算法

应用一种新的正则化方法建立了一类新的求解第一类Fredholm积分方程的正则化算法, 并借助Matlab软件给出了数值算例.数值结果与理论分析基本一致,而且表明文中建立的正则化比通常的Tikhonov正则化更精确.     

Linearization of class C for contractions on Banach spaces

In this work we prove a C¹-linearization result for contraction diffeomorphisms, near a fixed point, valid in infinite-dimensional Banach spaces. As an intermediate step, we prove a specific result of existence of invariant manifolds, which can be interesting by itself and that was needed on the proof of our main theorem. Our results essentially generalize some classical results by P. Hartman in finite dimensions, and a result of Mora-Sola-Morales in the infinite-dimensional case. It is shown that the result can be applied to some abstract systems of semilinear damped wave equations.     

Grow-up rate of solutions for a supercritical semilinear diffusion equation

We study solutions of the Cauchy problem for a supercritical semilinear parabolic equation which converge to a singular steady state from below as t→∞. We show that the grow-up rate of such solutions depends on the spatial decay rate of initial data.     

Examples of non-conjugated holomorphic vector fields and foliations

We consider germs of holomorphic vector fields near the origin of with a saddle-node singularity, and the induced singular foliations. In a previous article we described the invariants addressing the analytical classification of these vector fields. They split into three parts: a formal, an orbital and a tangential component. For a fixed formal class, the orbital invariant (associated to the foliation) was obtained by Martinet and Ramis; we give it an integral representation. We then derive examples of non-orbitally conjugated foliations by the use of a “first-step” normal form, whose first-significative jet is an invariant. The tangential invariant also admits an integral representation, hence we derive explicit examples of vector fields, inducing the same foliation, that are not mutually conjugated. In addition, we provide a family of normal forms for vector fields orbitally equivalent to the model of Poincaré-Dulac.     

The well-posedness of the Korteweg-de Vries-Benjamin-Ono equation

The well-posedness of the Cauchy problem to the generalized Korteweg-de Vries-Benjamin-Ono equation is considered. Local results for data in (s?−1/8) and the global well-posedness for data in are obtained if l=2. Moreover, for l=3, the problem is locally well-posed for data in H^s (s?1/4). The main idea is to use the Fourier restriction norm method.     

与A-调和方程有关的两个结果

给出两个与A 调和方程有关的结果 .第一个结果是一类A 调和方程的很弱解可由调和函数逼近 .另一个是变分积分弱极值的充分必要条件     

具连续变量脉冲差分方程解的振动性

考虑新的一类具有连续变量的脉冲差分方程x(t τ) - x(t) p(t)x(t - rτ) =0,x(tk τ) - x(tk) = bkx(tk),　t≥t0 -τ,t≠tk,t∈N(1),其中p(t)是[t0 -τ,∞]上的非负连续函数,τ>0,bk 是常数,r是正整数, 0≤t0 < t1 < t2 <…< tk <…且limk→∞tk =∞,获得了方程所有解振动的充分条件.     

一类混合型微分差分方程的周期解

利用Fenchel变换,我们推出一类微分差分方程存在周期解等价于某泛函具有临界点,并求出方程具有周期解的充分条件.