Title of article :
Seven common errors in finding exact solutions of nonlinear differential equations
Author/Authors :
Kudryashov، نويسنده , , Nikolai A.، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2009
Abstract :
We analyze the common errors of the recent papers in which the solitary wave solutions of nonlinear differential equations are presented. Seven common errors are formulated and classified. These errors are illustrated by using multiple examples of the common errors from the recent publications. We show that many popular methods in finding the exact solutions are equivalent each other. We demonstrate that some authors look for the solitary wave solutions of nonlinear ordinary differential equations and do not take into account the well - known general solutions of these equations. We illustrate several cases when authors present some functions for describing solutions but do not use arbitrary constants. As this fact takes place the redundant solutions of differential equations are found. A few examples of incorrect solutions by some authors are presented. Several other errors in finding the exact solutions of nonlinear differential equations are also discussed.
Keywords :
nonlinear evolution equation , Common error , Exp-function method , Truncated expansion method , Tanh-function method , Exact solution
Journal title :
Communications in Nonlinear Science and Numerical Simulation
Journal title :
Communications in Nonlinear Science and Numerical Simulation