本文通过把十二个Jacobi椭圆函数分类成四组,从而提出一个新的广义Jacobi椭圆函数展开法来构造非线性演化方程的精确双周期解。在数学软件Maple的帮助下,应用这个非常有效的方法求出了非线性演化方程的许多解,当模数m→0或1时,这些解退...本文通过把十二个Jacobi椭圆函数分类成四组,从而提出一个新的广义Jacobi椭圆函数展开法来构造非线性演化方程的精确双周期解。在数学软件Maple的帮助下,应用这个非常有效的方法求出了非线性演化方程的许多解,当模数m→0或1时,这些解退化为相应的孤立波解或三角函数解。In this letter, twelve Jacobi elliptic functions are divided into four groups, and a new general Jacobi elliptic function expansion method is proposed to construct abundant exact doubly periodic solutions of nonlinear evolution equations. As a result, with the aid of computer symbolic computation software (for example, Maple), many exact doubly periodic solutions are obtained which shows that this method is very powerful. When the modulus m→0 or 1, these solutions degenerate to the corresponding solitary wave solutions and trigonometric function (singly periodic) solutions.展开更多
Notions of quasi-Jacobi bialgebroid and its Dirac-Jacobi structure are introduced.The necessary and sufficient conditions for a maximal isotropic subbundle L to be a DiracJacobi structure are proved.Meanwhile several ...Notions of quasi-Jacobi bialgebroid and its Dirac-Jacobi structure are introduced.The necessary and sufficient conditions for a maximal isotropic subbundle L to be a DiracJacobi structure are proved.Meanwhile several special examples are presented.展开更多
文摘本文通过把十二个Jacobi椭圆函数分类成四组,从而提出一个新的广义Jacobi椭圆函数展开法来构造非线性演化方程的精确双周期解。在数学软件Maple的帮助下,应用这个非常有效的方法求出了非线性演化方程的许多解,当模数m→0或1时,这些解退化为相应的孤立波解或三角函数解。In this letter, twelve Jacobi elliptic functions are divided into four groups, and a new general Jacobi elliptic function expansion method is proposed to construct abundant exact doubly periodic solutions of nonlinear evolution equations. As a result, with the aid of computer symbolic computation software (for example, Maple), many exact doubly periodic solutions are obtained which shows that this method is very powerful. When the modulus m→0 or 1, these solutions degenerate to the corresponding solitary wave solutions and trigonometric function (singly periodic) solutions.
基金Supported by the Scientific Reseaxch Common Program of Beijing Municipal Commission of Education(SQKM201211232017)Supported by the Beijing Excellent Training Grant(2012D005007000005)Supported by the Funding Program for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality(11530500015)
文摘Notions of quasi-Jacobi bialgebroid and its Dirac-Jacobi structure are introduced.The necessary and sufficient conditions for a maximal isotropic subbundle L to be a DiracJacobi structure are proved.Meanwhile several special examples are presented.
