The extended simplest equation method is employed to solve new coupled Konno-Oono equation. By means of this scheme, we found new exact solution. The method is straight for ward, concise and effective, it can also be applied to other nonlinear solution in mathematical physics.

The improved generalized tanh-coth method is used in nonlinear sixth-order solitary wave equation. This method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. The new exact solutions consisted of trigonometric functions solutions, hyperbolic functions solutions, exponential functions solutions, and rational functions solutions. The numerical results were obtained with the aid of Maple.

In this paper, we consider the Zakharov-Kuznetsov-Benjamin Bona Mahony nonlinear evolution equation and use the variational iteration method combined with the improved generalized tanh-coth method. This method is a powerful and advantageous mathematical tool for establishing abundant exact traveling wave solutions of nonlinear partial differential equations. The new exact solutions consisted of trigonometric functions solutions, hyperbolic functions solutions, exponential functions solutions and rational functions solutions. We obtain exact solutions of the Zakharov-Kuznetsov-Benjamin-Bona-Mahony nonlinear evolution equation by using the variational iteration method combined with the improved generalized tanh-coth method.

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