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

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.