非线性粘弹性杆波动方程的精确解

Exact Solutions for Wave Equation of Nonlinear Viscoelastic Rod

应用推广的Tanh函数方法对非线性粘弹性杆波动方程进行了求解.得到了孤波解、有理数解、三角函数周期波解等一些不同形式的精确解.这种方法的主要思想是充分利用Riccati方程,用它的解去构造原方程的解,并且能从参数的符号准确地判断出行波解的类型和个数.从求解过程可以看出,该方法是一种简便、有效的方法,并且可用于求解其它非线性方程或方程组.

The wave equation of nonlinear viscoelastic rod was solved by the extended Tanh-function method. These exact solutions include solitary wave solutions, rational number solutions and trigono- metric function periodic wave solutions. The key idea of this method is to take full advantage of Riccati equation and use its solutions to construct the solutions of the original equation. The sign of the parameters can be used to exactly judge the numbers and types of these traveling wave solutions. The solving process shows that the extended Tanh-function method is simple, effective and it can be used for many other nonlinear equations or equation sets. Key words： extended Tanh-function method; nonlinear viscoelastic rod; wave equation; exact solution