基于函数$1/\cosh^n$的最简方程的非线性偏微分方程的孤波解
Solitary wave solutions of nonlinear partial differential equations based on the simplest equation for the function $1/\cosh^n$
摘要：
本文应用最简方程法求出了一类含有奇、偶阶单项式的非线性偏微分方程的精确孤立行波解。使用的最简单的方程是$f_ξ^2 = n^2(f^2 -f^{(2n+2)/n})$。所开发的方法说明了两个例子的类的非线性偏微分方程，其中包含：（一）只有单项式的奇数级相对于参与的衍生工具;（二）只有单项式的偶数级相对于参与的衍生工具。所得到的情况（i）的孤立波解包含Korteweg-deVries方程和修正Korteweg-deVries方程的孤立波解作为特例。
英文摘要：
The method of simplest equation is applied for obtaining exact solitary traveling-wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives. The used simplest equation is $f_ξ^2 = n^2(f^2 -f^{(2n+2)/n})$. The developed methodology is illustrated on two examples of classes of nonlinear partial differential equations that contain: (i) only monomials of odd grade with respect to participating derivatives; (ii) only monomials of even grade with respect to participating derivatives. The obtained solitary wave solution for the case (i) contains as particular cases the solitary wave solutions of Korteweg-deVries equation and of a version of the modified Korteweg-deVries equation.
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