EXACT SOLUTIONS FOR A REACTION DIFFUSION EQUATION BY USING THE GENERALIZED TANH METHOD

In this paper we present the generalized tanh method to obtain exact solutions of nonlinear partial differential equations. As a particular case, we obtain exact solutions for a reaction diffusion equation

New classes of nonlinearly self-adjoint evolution equations of third- and fifth-order

In a recent communication Nail Ibragimov introduced the concept of nonlinearly self-adjoint differential equation [N. H. Ibragimov, Nonlinear self-adjointness and conservation laws, J. Phys. A: Math. Theor., vol. 44, 432002, 8 pp., (2011)]. In the present communication a nonlinear self-adjoint classification of a general class of fifth-order evolution equation with time dependent coefficients is presented. As a result five subclasses of nonlinearly self-adjoint equations of fifth-order and four subclasses of nonlinearly self-adjoint equations of third-order are obtained. From the Ibragimov's theorem on conservation laws [N. H. Ibragimov, A new conservation theorem, J. Math. Anal. Appl., vol. 333, 311--328, (2007)] conservation laws for some of these equations are established

EXACT SOLUTIONS FOR A REACTION DIFFUSION EQUATION BY USING THE GENERALIZED TANH METHOD

In this paper we present the generalized tanh method to obtain exact solutions of nonlinear partial differential equations. As a particular case, we obtain exact solutions for a reaction diffusion equation

EXACT SOLUTIONS FOR A REACTION DIFFUSION EQUATION BY USING THE GENERALIZED TANH METHOD

In this paper we present the generalized tanh method to obtain exact solutions of nonlinear partial differential equations. As a particular case, we obtain exact solutions for a reaction diffusion equation

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

Symbolic computation of solutions for three generalized nonlinear partial differential eQuations by using the tanh method

Three nonlinear partial differential equations, namely, the standard KdV equation, the Boussinesq equation and the generalized fifthorder KdV equation are considered here from of point the view of construct exact solutions for them. The equations that we consider here are in its most general form. New exact solutions which include periodic and soliton solutions are formally derived by using the tanh method. The programming language Matematica is used