On modified method of simplest equation for obtaining exact and approximate solutions of nonlinear PDEs: The role of the simplest equation

Publication year: 2011
Source: Communications in Nonlinear Science and Numerical Simulation, Volume 16, Issue 11, November 2011, Pages 4215-4231

Nikolay K., Vitanov

The modified method of simplest equation is powerful tool for obtaining exact and approximate solutions of nonlinear PDEs. These solutions are constructed on the basis of solutions of more simple equations called simplest equations. In this paper we study the role of the simplest equation for the application of the modified method of simplest equation. We follow the idea that each function constructed as polynomial of a solution of a simplest equation is a solution of a class of nonlinear PDEs. We discuss three simplest equations: the equations of Bernoulli and Riccati and the elliptic equation. The applied algorithm is…

 Highlights: ► The role of the simplest equation the application of the method of simplest equation is studied. ► 3 simplest equations are discussed: equations of Bernoulli, Riccati and elliptic equation. ► Each polynomial of solution of a simplest equation is solution of a class of nonlinear PDEs.