Comment on: 'Some exact solutions of KdV equation with variable coefficients' [Commun Nonlinear Sci Numer Simul 2011; 16:1783-86]

摘要

It is shown that in the commented paper the exact solutions were found only for those variable-coefficient KdV equations which are reduced to the classical (constant-coefficient) KdV equation by point transformations, and these solutions are preimages of well-known traveling wave solutions of the KdV equation with respect to the corresponding point transformations. The equivalence-based approach suggested in [Popovych RO, Vaneeva 00. More common errors in finding exact solutions of nonlinear differential equations: Part 1. Commun Nonlinear Sci Numer Simul 2010; 15:3887-99] allows one to obtain more results. This disproves the relevance of the extended mapping transformation method for the class of equations under consideration.