[PDF] Top 20 New Jacobi Elliptic Function Solutions for Coupled KdV-mKdV Equation

... wave solutions of nonlinear evolution equations(NLEEs) has been an interesting and hot topic in mathematics physics for a long ...wave solutions of NLEEs have been established ...all solutions for ... See full document

... commutator equation [ , ] Q P = 0 of partial differential operators Q P , invariant under the action of a Weyl group, and obtained many of elliptic function ...Painlevé equation is not only a ... See full document

... the KdV and the mKdV ...wave solutions and doubly periodic wave solutions []; Qin et ...wave solutions for the system ...theta function and the Hirato bilinear method will be ... See full document

... [24], Jacobi elliptic function expansion [25], the F-expansion [26], the exp-function expansion method [27], (G /G)- expansion method [28–31], and so on, but there is no unified method that can ... See full document

... exact solutions of partial differential equations in fractional case, and proposed a new fractional Riccati sub-equation method, where the sub-equation used is the fractional Riccati ... See full document

... hyperbolic function method [10],the tanh method and its extension [11-13], the ...the Jacobi elliptic function expansion method [21],and so ...many new exact solutions which we ... See full document

... a new fractional Jacobi elliptic equation method to seek exact solutions of fractional partial differential ...differential equation can be turned into another fractional ordinary ... See full document

... simplest equation method [] and the Jacobi elliptic function method [] are later employed to obtain some exact solutions of ...the new conservation theorem [] and the ... See full document

... wave solutions of the KP-BBM equation, the (3 + 1)-dimensional potential-YTSF equation, the (2 + 1)-dimen- sional Zakharov-Kuznetsov ...wave solutions of the strain wave equation in ... See full document

... differential equation (7) is then integrated as long as all terms contain derivatives, where we neglect the integration ...The solutions of many nonlinear equations can be expressed in the form [13]: ... See full document

... exact solutions and to develop some efficient ...differential equation can only be efficiently solved by different corresponding ...the Jacobi elliptic function expan- sion method [7], ... See full document

... analytic solutions for NPDEssome methods have proposed, such as the homotopy analysis method [1, 2], three- wave method [3], extended homoclinic test approach [4], the improved F-expansion method [5], the ... See full document

... auxiliary equation expansion method and its algorithm is proposed by studying a second order nonlinear ordinary differential equation with a four-degree ...(GBL) equation with any order. As a result, ... See full document

... auxiliary equation method, many kinds of smooth type soliton, tense type soliton and peak soliton and so on new solutions of the nonlinear evolution equations have been obtained ...the ... See full document

... combined KdV–mKdV equation. However, numerical solutions are more accurate for h = ...the elliptic points of r(x, t), and the ideal node point of r(x, t) is x = ... See full document

... that they are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role in finding exact solutions ... See full document

... the Jacobi elliptic function method [14], the A domian decomposition method [15] [16], the method of bi- furcation of planar dynamical systems [17] [18], the inverse scattering transform method [19], ... See full document

... The rest of the article is organized as follows: In Section 2, the method has been discussed. In Section 3, we apply this method to the positive Gardner-KP equation. In Section 4, the physical explanations of the ... See full document

... periodic solutions of the KDV type of equation with respect to time variable with periodic external ...original equation to the integral ...the equation is proved by the fixed point ... See full document

... (KdV) equation will be obtained with the help of the reductive perturbation method, which admits a double layer structure in current plasma ...of new analytical method we obtain the new exact ... See full document