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标题：Extended tanh-function method and its applications to nonlinear equations
来源：《物理快报A》2000年277卷4-5期212-218页
作者：复旦大学数学研究所 En-Gui Fan（范恩贵）
Research Fronts: NEW INTEGRABLE COUPLED NONLINEAR EVOLUTION EQUATIONS; NEW EXPLICIT SOLITARY WAVE SOLUTIONS; NEW EXPLICIT TRAVELLING WAVE SOLUTIONS; NONLINEAR WAVE EQUTIONS; PERIODIC WAVE SOLUTIONS
领域：物理
摘要：An extended tanh-function method is proposed for constructing multiple travelling wave solutions of nonlinear partial differential equations (PDEs) in a unified way. The key idea of this method is to take full advantages of a Riccati equation involving a parameter and use its solutions to replace the tanh function in the tanh-function method. It is quite interesting that the sign of the parameter can be used to exactly judge the numbers and types of these travelling wave solutions. In addition, by introducing appropriate transformations, it is shown that the extended tanh-function method still is applicable to nonlinear PDEs whose balancing numbers may be any nonzero real numbers. Some illustrative equations are investigated by this means and new travelling wave solutions are found.
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