Extended F-expansion method and periodic wave solutions for the generalized Zakharov equations

New Exact Analytical Solutions for the General KdV Equation with Variable Coefficients

“…Our method proposed here is more general than the extended Riccati equation rational expansion method [6], the extended auxiliary function method [8], the generalized F-expansion method [13], the generalized Jacobi elliptic functions expansion method [14,15], and many other algebra expansion methods [9,10,12 …”

“…The investigation of exact solutions of NLPDEs plays an important role in the study of these phenomena such as the nonlinear dynamics and the mechanism behind the phenomena. With the development of soliton theory, many powerful methods for obtaining exact solutions of NLPDEs have been presented, such as inverse scattering transformation [1], Hirota bilinear method [2], Bäcklund transformation [3], Darboux transformation [4], homotopy perturbation method [5], extended Riccati equation rational expansion method [6], asymptotic methods [7], extended auxiliary function method [8], algebraic method [9], Jacobi elliptic function expansion method [10],and so on [11][12][13].…”

“…In [16], Hong et al proposed an improved general mapping deformation method to obtain generalized exact solutions of the general KdV equation with variable coefficients (GVKDV). Which is more general than many other algebra expansion methods [6,[8][9][10][11][12][13][14][15] etc. The solution procedure of this method, by the help of Matlab or Mathematica, is of the utmost simplicity, and this method can be easily extended to all kinds of NLPDEs.…”

Exp-Function Method with Computerized Symbolic Computation for New Exact Solution of Burger's Equation

“…In the past several decades, some effective methods equipped with the powerful computerized symbolic computation systems like Mathematica or Maple have been proposed for nonlinear PDEs [1][2][3][4][5][6][7][8]. It is shown that these symbolic computation systems become indispensable auxiliary tools for solving complex PDEs or constructing more general solutions of PDEs.…”

Exact Traveling Wave Solutions of Nonlinear PDEs in Mathematical Physics

“…For instance, the nonlinear wave phenomena observed in fluid dynamics, plasma and optical fibers are often modeled by the bell shaped sech solutions and the kink shaped tanh solutions. Many effective methods have been presented, such as inverse scattering transform method [1], Bäcklund transformation [2], Darboux transformation [3], Hirota bilinear method [4], variable separation approach [5], various tanh methods [6][7][8][9], homogeneous balance method [10], similarity reductions method [11,12],   G G  -expansion method [13], the reduction mKdV equation method [14], the tri-function method [15,16], the projective Riccati equation method [17], the Weierstrass elliptic function method [18], the Sine-Cosine method [19,20], the Jacobi elliptic function expansion [21,22], the complex hyperbolic function method [23], the truncated Painleve' expansion [24], the F-expansion method [25], the rank analysis method [26], the ansatz method [27,28], the exp-function expansion method [29], the sub-ODE method [30], and so on.…”