Solitons and other solutions to the nonlinear Bogoyavlenskii equations using the generalized Riccati equation mapping method

Abstract

Recently, the authors of the article (Zahran and khater in Appl Math Model 40:1769–1775, 2016) have applied the modified extended tanh-function method to the nonlinear Bogoyavlenskii equations and found very few special solutions. In our article, we generalize this work by showing that the modified extended tanh-function method is just a special case of the generalized Riccati equation mapping method. Many families of exact solutions of the nonlinear Bogoyavlenskii equations have been found using the generalized Riccati equation mapping method. Bright–dark–singular soliton solutions and other solutions are obtained. Comparing our results with the well-known results are given.