最简方程修正法方法论的新发展及其应用
New developments of the methodology of the Modified method of simplest equation with application
摘要：
本文讨论了求非线性偏微分方程精确解析解的修正最简方程法的一个推广。该扩展包括使用的可能性：（i）一个以上的最简单的方程;（ii）关系，其中包含作为特殊情况下的关系所使用的广田\cite{hirota}和关系中使用的前一版本的方法;（iii）转换的解决方案，其中包含作为特殊情况下的可能性使用的Painleve扩展;（iv）一个以上的平衡方程。讨论的版本的方法允许：获得多孤子解的非线性偏微分方程，如果这样的解决方案确实存在，并获得特定的解决方案的不可积的非线性偏微分方程。的方法的应用的例子进行了讨论。
英文摘要：
We discuss an extension of the modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations. The extension includes the possibility for use of: (i) more than one simplest equation; (ii) relationship that contains as particular cases the relationship used by Hirota \cite{hirota} and the relationship used in the previous version of the methodology; (iii) transformation of the solution that contains as particular case the possibility of use of the Painleve expansion; (iv) more than one balance equation. The discussed version of the methodology allows: obtaining multi-soliton solutions of nonlinear partial differential equations if such solutions do exist and obtaining particular solutions of nonintegrable nonlinear partial differential equations. Examples for the application of the methodology are discussed.
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