Application of the Cole-Hopf Transformation for Finding Exact Solutions to Several Forms of the Seventh-Order KdV Equation

We use a generalized Cole-Hopf transformation to obtain a condition that allows us to find exact solutions for several forms of the general seventh-order KdV equation (KdV7). A remarkable fact is that this condition is satisfied by three well-known particular cases of the KdV7. We also show some solutions in these cases. In the particular case of the seventh-order Kaup-Kupershmidt KdV equation we obtain other solutions by some ansatzes different from the Cole-Hopf transformation

Improved G\u27/G-Expansion Method and Comparing with Tanh-Coth Method

In this paper, improved G\u27/G-expansion and tanh-coth methods for solving partial differential equations are compared. It has been shown that the tanh-coth method is a special case of the improved G\u27/G-expansion method. For illustration and more explanation of the idea, exact solutions of the Burgers and Boussinesq equations are obtained by improved G\u27/G-expansion and the results obtained compared with those of tanh-coth method

Stability Analysis for Some Nonlinear Fifth-Order Equations

The main purpose of this work is to obtain many travelling wave solutions for general KaupKuperschmidt (KK), general Lax, general Sawada-Kotera (SK) and general Ito equations with the aid of symbolic computation by employing the extended direct algebraic method. The stability of these solutions and wave motion have been analyzed by illustrative plots

Conservation laws for a generalized seventh order KdV equation

In this paper, by applying the multiplier method we obtain a complete classification of low-order local conservation laws for a generalized seventh-order KdV equation depending on seven arbitrary nonzero parameters. We apply the Lie method in order to classify all point symmetries admitted by the equation in terms of the arbitrary parameters. We find that there are no special cases of the parameters for which the equation admits extra symmetries, other than those that can be found by inspection (scaling symmetry and space and time translation symmetries). We consider the reduced ordinary differential equations and we determined all integrating factors of the reduced equation from the combined x- and t- translation symmetries. Finally, we observe that all integrating factors arise by reduction of the low-order multipliers of the generalized seventh-order KdV equation.7 página

New periodic and soliton solutions by application of Exp-function method for nonlinear evolution equations

AbstractIn this letter, the Kaup–Kupershmidt, (2+1)-dimensional Potential Kadomtsev–Petviashvili (shortly PKP) equations are presented and the Exp-function method is employed to compute an approximation to the solution of nonlinear differential equations governing the problem. It has been attempted to show the capabilities and wide-range applications of the Exp-function method. This method can be used as an alternative to obtain analytic and approximate solution of different types of differential equations applied in engineering mathematics

Computing Exact Solutions to a Generalized Lax-Sawada-Kotera-Ito Seventh-Order KdV Equation

The Cole-Hopf transform is used to construct exact solutions to a generalization of both the seventh-order Lax KdV equation (Lax KdV7) and the seventh-order Sawada-Kotera-Ito KdV equation (Sawada-Kotera-Ito KdV7)