NEW EXPLICIT AND EXACT TRAVELLING WAVE SOLUTIONS FOR A COMPOUND KdV－BURGERS EQUATION

In this paper, new explicit and exact travelling wave solutions for a compound KdV－Burgers equation are obtained by using the hyperbola function method and the Wu elimination method, which include new solitary wave solutions and periodic solutions. Particularly important cases of the equation, such as the compound KdV, mKdV－Burgers and mKdV equations can be solved by this method. The method can also solve other nonlinear partial differential equations.     

含外力项的广义KdV方程的新自Darboux变换和显式解析解

基于 Ｒｉｃｃａｔｉ形式的 Ｌａｘ对,本文推得了含外力项的广义 ＫｄＶ方程的新自Ｄａｒｂｏｕｘ变换．当应用这个变换时,仅需要做积分,就能获得一系列显示解析解,其中包含类孤波解．这种途径对于寻找非线性发展方程新的具有物理意义的解或许是有用的．     

非线性耦合标量场方程显式解析解的研究

利用两种不同的变换,获得了一类非线性耦合标量场方程的若干类型的精确解析解,其中包括孤子解、奇性孤波解和三角函数解,从而丰富了方程解的内容。这些结论可以应用于其它的非线性方程。此外还纠正了一些文献的部分结论。     

新的耦合mKdV方程族及其Liouville可积的无限维Hamilton结构

根据第Ⅱ屠格式,从一个特征值问题出发,本文推得了一族新的耦合ｍＫｄＶ方程,然后用迹恒等式人出了其无限维Ｈａｍｉｌｔｏｎ结构。最后证明了该Ｈａｍｉｌｔｏｎ方程族是Ｌｉｏｕｖｉｌｌｅ可积的,并且有无穷多个彼此对合的公共守恒密度。     

Two types of new algorithms for finding explicit analytical solutions of nonlinear differential equations

ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒｓｅｖｅｒａｌｈｕｎｄｒｅｄｙｅａｒｓ,ｉｔｈａｓｂｅｅｎｂｏｔｈｉｍｐｏｒｔａｎｔａｎｄｄｉｆｆｉｃｕｌｔｐｒｏｊｅｃｔｔｏｃｏｎｓｔｒｕｃｔｔｈｅａｎａｌｙｔｉｃａｌｓｏｌｕｔｉｏｎｓｆｏｒｎｏｎｌｉｎｅａｒｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ.Ｍａｎｙｍａｔｈｅｍａｔｉｃｉａｎｓａｎｄｔｈｅｏｒｅｔｉｃａｌｐｈｙｓｉｃｉｓｔｓｈａｖｅｄｏｎｅａｌｏｔｏｆｗｏｒｋ[1～ 5 ].Ｈｏｗｅｖｅｒ,ｔｈｅｒｅｅｘｉｓｔｌｏｔｓｏｆｉｍｐｏｒｔａｎｔａｎｄｂｅｉｎｇｏｆｐ…     

On a new algorithm of constructing solitary wave solutions for systems of nonlinear evolution equations in mathematical physics

ＩｎｔｒｏｄｕｃｔｉｏｎＳｏｌｖｉｎｇｎｏｎｌｉｎｅａｒｅｑｕａｔｉｏｎｓｉｓａｌｗａｙｓａｖｅｒｙｉｎｔｅｒｅｓｔｉｎｇｓｕｂｊｅｃｔｆｏｒｍａｔｈｅｍａｔｉｃｉａｎａｎｄｐｈｙｓｉｃｉａｎ ,ｉｎｐａｒｔｉｃｕｌａｒ,ｓｏｌｉｔａｒｙｗａｖｅｓｏｌｕｔｉｏｎｓｆｏｒｎｏｎｌｉｎｅａｒｅｑｕａｔｉｏｎｓａｒｅｏｆｂｏｔｈｔｈｅｏｒｅｔｉｃａｌａｎｄｐｒａｃｔｉｃａｌｉｍｐｏｒｔａｎｃｅ.Ｒｅｃｅｎｔｌｙ ,Ｙａｎ[1]ｏｂｔａｉｎｅｄａｔｒａｎｓｆｏｒｍａｔｉｏｎｄｉｒｅｃｔｌｙｆｒｏｍｔｈｅｆａｍｏ…     

广义组合KdV-mKdV方程的显式精确解

Abstract. With the aid of Mathematica and Wu-elimination method,via using a new generalizedansatz and well-known Riccati equation,thirty-two families of explicit and exact solutions forthe generalized combined KdV and mKdV equation are obtained,which contain new solitarywave solutions and periodic wave solutions. This approach can also be applied to other nonlinearevolution equations.     

Applications of fractional exterior differential in three-dimensional space

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｇｅｎｅｒａｌｉｚｅｄｉｎｔｅｇｒａｔｉｏｎａｎｄｄｉｆｆｅｒｅｎｔｉａｔｉｏｎｔｈｅｑｕｅｓｔｉｏｎｏｆｅｘｔｅｎｓｉｏｎｏｆｍｅａｎｉｎｇｉｓ:ｃａｎｔｈｅｍｅａｎｉｎｇｏｆｄｅｒｉｖａｔｉｖｅｓｏｆｉｎｔｅｇｒａｌｏｒｄｅｒｄｎｙ/ｄｘｎｂｅｅｘｔｅｎｄｅｄｔｏｈａｖｅｍｅａｎｉｎｇｗｈｅｒｅｎｉｓａｎｙｎｕｍｂｅｒ (ｅ .ｇ .,ｉｒｒａｔｉｏｎａｌ,ｆｒａｃｔｉｏｎｏｒｃｏｍｐｌｅｘ) ?Ｉｎ 1 695Ｌｅｉｂｎｉｚｉｎｖｅｎｔｅｄａｂｏｖｅｎｏｔａｔｉｏｎ .Ｅｕｌａｒａ…     

变形色散水波方程的Auto-B(a)cklund变换、多孤子解和有理分式解

利用未知数变换并借助Mathematica软件,给出了变形色散水波方程的Auto-B(a)cklund变换以及它与热传导方程和线性方程之间的Darboux变换.进而用此变换,获得了变形色散水波方程的多孤子解、有理分式解及其他精确解.这种思路也适用于其他的非线性方程.