一个(3+1)维非线性方程的B(a)cklund变换和精确解

利用双Bell多项式方法构造了一个(3+1)维非线性方程的双线性形式,得到了该方程的双线性Bcklund变换和相应的Lax对.同时利用Riemann theta函数,获得了该方程的周期波解.     

带源的超对称KdV方程的双线性B(a)cklund变换

给出经典带源的KdV方程的一个超对称形式,利用Hirota双线性方法得到它的双线性形式,并从双线性形式出发利用一些双线性算子恒等式构造了它的双线性B(a)cklund变换.     

(2+1)维非线性Schr(o)dinger型方程的同宿轨道

研究了几类(2 1)维非线性Schr(o)dinger型方程同宿轨道的问题.利用Hirota双线性算子方法, 通过给出的相关变换, 得到了包括(2 1)维的长短波相互作用方程, 广义Zakharov方程, Mel'nikov方程和g-Schr(o)dinger方程的同宿轨道解的显式解析表达式,从而讨论了这些方程的同宿轨道.     

(2+1)维广义破碎孤子方程的Painlev(?)可积性和多孤子解

借助符号计算软件,利用简化的Weiss-Tabor-Carnevale(WTC)方法,对广义的(2+1)维破碎孤子方程进行了Painleve检验,并得到了该方程的可积条件.基于多维Bell多项式的相关理论知识,导出了该方程的Hirota双线性形式,并构造出了方程的多孤子解.     

(3+1)维变系数Kudryashov-Sinelshchikov(K-S)方程的同宿呼吸波解和高阶怪波解

基于Hirota双线性方法,利用拓展的同宿呼吸检验法得到了(3+1)维变系数Kudryashov-Sinelshchikov(K-S)方程的同宿呼吸波解,对该解的参数选取合适的数值,可得到不同结构的同宿呼吸波.通过对同宿呼吸波解的周期取极限,推导出方程的怪波解.最后,构造出一个特殊的高阶多项式作为测试函数,求得该方程的一阶怪波解和二阶怪波解.     

新的变系数可积耦合非线性Schr(o)dinger方程及其孤子解

基于延拓结构和Hirota双线性方法研究了广义的变系数耦合非线性Schr(o)dinger方程.首先导出了3组新的变系数可积耦合非线性Schr(o)dinger方程及其线性谱问题(Lax对),然后利用Hirota双线性方法给出了它们的单、双向量孤子解.这些向量孤子解在光孤子通讯中有重要的应用.     

(2+1)-维变系数CDGKS方程的Bcklund变换及Gramm-type Pfaffian解

孤立子在非线性的流体力学、等离子物理学、光学、生物学等领域有广泛的应用.将(2+1)维常系数CDGKS方程扩展为(2+1)维变系数CDGKS方程,利用双线性方法求出了该方程的Bcklund变换,进一步求出变系数CDGKS方程及其修正变系数CDGKS方程的Gramm-type Pfaffian解,从而解决了变系数孤立子方程的精确解.     

(2+1)维广义Camassa-Holm-Kadomtsev-Petviashvili方程的三阶和四阶怪波解

简明地构造了(2+1)维广义Camassa-Holm-Kadomtsev-Petviashvili,(gCHKP)方程的双线性形式,进一步利用符号计算方法,得到方程的三阶和四阶怪波解.结果表明辅助函数中的参数可以控制怪波的形状.     

B(a)cklund变换与n孤子解

本文首先证明了KdV方程与sine-Gordon方程不同形式的B(a)cklund变换是相互等价的;其次从双线性导数形式的B(a)cklund变换出发给出多孤子解的Hirota表示与Wronski行列式表示,并利用Vandermonde行列式说明这两种孤子解的表示是一致的.     

广田双线性方法与(3+1)维Jimbo-Miwa-Like方程的几种新解

基于广田双线性方法,将(3+1)维Jimbo-Miwa-Like方程化为双线性形式,在此基础上,首先利用试探函数法与符号计算系统Mathematica,获得了方程的由指数函数、三角函数和双曲函数形式的单函数解;另外,获得了由三角函数、指数函数与双曲函数两两组合的复合型解.最后通过选取适当的参数,做出一部分精确解的图形来说明它们的性质.     

The matrix equationa(x∘y)=a(x)+a(x)a(y)+a(y)

Aequationes mathematicae -     

(a)-spaces and selectively (a)-spaces from almost disjoint families

We investigate a selective version of property (a) and prove a number of results showing that, under certain set theoretical conditions, (a) spaces and selectively (a) spaces behave in a very similar way, at least for separable spaces. Several results regarding the presence of the referred selective version in spaces from almost disjoint families are established; in particular, we give a combinatorial characterization of such presence. Consistent set theoretical hypotheses implying equivalence between being (a) and being selectively (a) within the referred class are presented, as well as hypotheses implying non-equivalence. We also show that the Continuum Hypothesis is independent of the statement asserting the above mentioned equivalence. The paper finishes by presenting some notes and questions on the role of set theoretical assumptions in the subject.     

K(a)hler Finsler Metrics Are Actually Strongly K(a)hler

In this paper,the K(a)hler conditions of the Chern-Finsler connection in complex Finsler geometry are studied,and it is proved that K(a)hler Finsler metrics are actually strongly K(a)hler.     

Reducibility of polynomials a0(x) + a1 (x)y + a2 (x) y2 modulo p

Let f=a₀(x)+a₁(x)y+a₂(x)y² ? \Bbb Z[x,y]f=a_0(x)+a_1(x)y+a_2(x)y^2\in {\Bbb Z}[x,y] be an absolutely irreducible polynomial of degree m in x. We show that the reduction f mod p will also be absolutely irreducible if p 3 c_m·H(f)^e_mp\ge c_m\cdot H(f)^{e_m} where H (f) is the height of f and e₁ = 4,e₂ = 6, e₃ = 6 [2/3]{2}\over{3} and e_m = 2 m for m S 4. We also show that the exponents e_m are best possible for m 1 3m\ne 3 if a plausible number theoretic conjecture is true.     

On commutator subspaces of GF(p a )SL2(p a )-modules

Let p a prime, X = SL₂(p^a) and K = GF(p^a). For S a Sylow p-subgroup of X, we explicitly describe the structure of the commutator series of S on each of the irreducible KX-modules.Received: 28 April 2004