We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion ...We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the variant Boussinesq equations. When the modulus m approaches 1 and 0, the hyperbolic function solutions (including the solitary wave solutions) and trigonometric solutions are also given respectively.展开更多
With the aid of a class of nonlinear ordinary differential equation (ODE) and its various positive solutions,four types of exact solutions of the generalized derivative nonlinear Schrdinger equation (GDNLSE) have been...With the aid of a class of nonlinear ordinary differential equation (ODE) and its various positive solutions,four types of exact solutions of the generalized derivative nonlinear Schrdinger equation (GDNLSE) have been foundout,which are the bell-type solitary wave solution,the algebraic solitary wave solution,the kink-type solitary wavesolution and the sinusoidal traveling wave solution,provided that the coefficients of GDNLSE satisfy certain constraintconditions.For more general GDNLSE,the similar results are also given.展开更多
现在的纸的目的是双重的。首先，射影的 Riccatiequations (PRE 为短) 借助于一条线性化的定理被解决，它在文学被知道。基于 PRE 的系数的符号和值，有 PRE 的二个任意的参数的解决方案能被夸张函数，三角法的函数，和合理函数分别地...现在的纸的目的是双重的。首先，射影的 Riccatiequations (PRE 为短) 借助于一条线性化的定理被解决，它在文学被知道。基于 PRE 的系数的符号和值，有 PRE 的二个任意的参数的解决方案能被夸张函数，三角法的函数，和合理函数分别地表示，同时，在 PRE 的每个答案的部件之间的关系也被实现。第二，某 nonlinearPDEs 的更多的新旅行波浪解决方案例如汉堡包方程， mKdV 方程，NLS~+方程，等等，新哈密尔顿振幅方程被使用亚颂诗获得方法，在哪个因为这个方法的 Sub-ODEs.The 关键想法是非线性的 PDE 的旅行波浪答案能被一个多项式在二个变量表示， PRE 被拿，它是 PRE 的每个答案的部件，如果在在方程的更高的顺序衍生物和非线性的术语之间的同类的平衡被考虑。展开更多
我们在场为在数学物理发现非线性的进化方程的周期的波浪答案的一个扩大 F 扩大方法。由使用扩大 F 扩大方法，各种各样的 Jacobi 椭圆形的功能为 theKlein-Gordon-Schroedinger 方程表示的许多周期的波浪答案被获得。在限制盒子中，方...我们在场为在数学物理发现非线性的进化方程的周期的波浪答案的一个扩大 F 扩大方法。由使用扩大 F 扩大方法，各种各样的 Jacobi 椭圆形的功能为 theKlein-Gordon-Schroedinger 方程表示的许多周期的波浪答案被获得。在限制盒子中，方程的独居的波浪解决方案和三角法的函数解决方案也被获得。展开更多
基金The project supported in part by Natural Science Foundation of Henan Province of China under Grant No. 2006110002 and the Science Foundation of Henan University of Science and Technology under Grant No. 2004ZD002
基金河南省自然科学基金，河南省教育厅自然科学基金，the Science Foundation of Henan University of Science and Technology
文摘We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the variant Boussinesq equations. When the modulus m approaches 1 and 0, the hyperbolic function solutions (including the solitary wave solutions) and trigonometric solutions are also given respectively.
基金the Natural Science Foundation of Education Department of Henan Province of China under Grant No.2007110010the Science Foundation of Henan University of Science and Technology under Grant Nos.2006ZY-001 and 2006ZY-011
文摘With the aid of a class of nonlinear ordinary differential equation (ODE) and its various positive solutions,four types of exact solutions of the generalized derivative nonlinear Schrdinger equation (GDNLSE) have been foundout,which are the bell-type solitary wave solution,the algebraic solitary wave solution,the kink-type solitary wavesolution and the sinusoidal traveling wave solution,provided that the coefficients of GDNLSE satisfy certain constraintconditions.For more general GDNLSE,the similar results are also given.
基金The project supported in part by the Natural Science Foundation of Education Department of Henan Province of China under Grant No. 2006110002 and the Science Foundations of Henan University of Science and Technology under Grant Nos. 2004ZD002 and 2006ZY001
文摘现在的纸的目的是双重的。首先，射影的 Riccatiequations (PRE 为短) 借助于一条线性化的定理被解决，它在文学被知道。基于 PRE 的系数的符号和值，有 PRE 的二个任意的参数的解决方案能被夸张函数，三角法的函数，和合理函数分别地表示，同时，在 PRE 的每个答案的部件之间的关系也被实现。第二，某 nonlinearPDEs 的更多的新旅行波浪解决方案例如汉堡包方程， mKdV 方程，NLS~+方程，等等，新哈密尔顿振幅方程被使用亚颂诗获得方法，在哪个因为这个方法的 Sub-ODEs.The 关键想法是非线性的 PDE 的旅行波浪答案能被一个多项式在二个变量表示， PRE 被拿，它是 PRE 的每个答案的部件，如果在在方程的更高的顺序衍生物和非线性的术语之间的同类的平衡被考虑。
基金The project supported by the Natural Science Foundation of Eduction Committce of Henan Province of China under Grant No. 2003110003, and the Science Foundation of Henan University of Science and Technology under Grant Nos. 2004ZD002 and 2004ZY040
文摘我们在场为在数学物理发现非线性的进化方程的周期的波浪答案的一个扩大 F 扩大方法。由使用扩大 F 扩大方法，各种各样的 Jacobi 椭圆形的功能为 theKlein-Gordon-Schroedinger 方程表示的许多周期的波浪答案被获得。在限制盒子中，方程的独居的波浪解决方案和三角法的函数解决方案也被获得。
