Note on same result of different ansätz based on extended tanh-function method for nonlinear models

摘要

The same result of different ansätz based on extended tanh-function method for nonlinear models is firstly reported. As an example, we obtain eleven kinds of variable separation solutions of variable-coefficient Boiti–Leon–Pempinelli system based on the extended tanh-function method by considering three different ansätz, namely, positive power-form ansatz, positive and negative power-symmetric ansatz and radical sign combined ansatz. By careful analysis, we find that these seemly independent variable separation solutions are essentially same. From this perspective, different ansätz are not really effective to construct so-called “new” solutions. Therefore, we should check carefully solutions obtained by the same method with different ansätz, and avoid casually asserting these essentially same “new” solutions.