Exact solutions of the generalized K(m,m)K(m,m) equations

Family of equations, which is the generalization of the $K(m,m)$ equation, is considered. Periodic wave solutions for the family of nonlinear equations are constructed

Application of the generalized Kudryashov method to the Eckhaus equation

In this paper, the generalized Kudryashov method is presented to seek exact solutions of the Eckhaus equation. From these solutions, we can derive solitary wave solutions as a special case. The proposed method is direct, effective and convenient and can be applied to many nonlinear evolution equations in mathematical physics

New exact solutionsand numerical approximations of the generalized kdv equation

This paper is devoted to create new exact and numerical solutions of the generalized Korteweg-de Vries (GKdV) equation with ansatz method and Galerkin finite element method based on cubic B-splines over finite elements. Propagation of single solitary wave is investigated to show the efficiency and applicability of the proposed methods. The performance of the numerical algorithm is proved by computing L2 and L∞ error norms. Also, three invariants I1, I2, and I3 have been calculated to determine the conservation properties of the presented algorithm. The obtained numerical solutions are compared with some earlier studies for similar parameters. This comparison clearly shows that the obtained results are better than some earlier results and they are found to be in good agreement with exact solutions. Additionally, a linear stability analysis based on Von Neumann’s theory is surveyed and indicated that our method is unconditionally stable