Filiz Ali, Ekici Mehmet, Sonmezoglu Abdullah
Department of Mathematics, Faculty of Science and Arts, Adnan Menderes University, 09010 Aydin, Turkey.
Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, Turkey.
ScientificWorldJournal. 2014 Jan 29;2014:534063. doi: 10.1155/2014/534063. eCollection 2014.
F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics.
提出了F展开法来寻求非线性演化方程的精确解。借助符号计算，我们选取带源的薛定谔 - 科特韦格 - 德弗里斯方程来说明该方法的有效性和优势。得到了许多雅可比椭圆函数解，包括魏尔斯特拉斯椭圆函数解。当雅可比椭圆函数的模m分别趋近于1和0时，还分别得到了类孤子解和三角函数解。该方法对于数学物理中的非线性演化方程是一种直接、简洁、有前景且强大的方法。
