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Construction of simple equations with known exact solutions is very important for the applications of the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear differential equations. Such simple equations can be used in SEsM for obtaining exact solutions of more complicated nonlinear differential equations. We discuss several transformations which lead to nonlinear equations with known exact solutions. The idea of the study is based on the idea which led to the Hopf-Cole transformation.

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Recent Developments in the Methodology of the Simple Equations Method (SEsM) for Obtaining Exact Solutions of Nonlinear Differential Equations

  • 会议论文

  • 发表日期：

    2025年

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  • Nikolay K. Vitanov

摘要

Construction of simple equations with known exact solutions is very important for the applications of the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear differential equations. Such simple equations can be used in SEsM for obtaining exact solutions of more complicated nonlinear differential equations. We discuss several transformations which lead to nonlinear equations with known exact solutions. The idea of the study is based on the idea which led to the Hopf-Cole transformation.