Alvaro H. Salas

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.

The Cole–Hopf transformation and improved tanh–coth method applied to new integrable system (KdV6)

Abstract In this paper, we study a new coupled system (KdV6) from the point of view of constructing exact solutions for it by using the Cole–Hopf transformation and one improved tanh–coth method. Traveling wave solution which includes periodic and soliton solutions are formally derived.

SOME SOLUTIONS FOR A TYPE OF GENERALIZED SAWADA-KOTERA EQUATION

Abstract In this paper we consider a particular case of the general KdV fifth-order differential equation. Some solutions are obtained by the projective Riccati equation method with the aid of

Symbolic computation of solutions for a forced Burgers equation

In this paper we give exact solutions for a forced Burgers equation. We make use of the generalized Cole-Hopf transformation and the traveling wave method.

Exact solutions for the general fifth KdV equation by the exp function method

In this letter we solve the general fifth KdV equation with the aid of a computer by using the exp function method. Some new solutions for the Ito equation are given.

Exact Solutions for the Generalized BBM Equation with Variable Coefficients

The variational iteration algorithm combined with the exp-function method is suggested to solve the generalized Benjamin-Bona-Mahony equation (BBM) with variable coefficients. Periodic and soliton solutions are formally derived in a general form. Some particular cases are considered.

Computing exact solutions for some fifth KdV equations with forcing term

Abstract In this paper, the extended tanh method is used to construct generalized soliton solutions, periodic solutions and rational solutions for the Sawada–Kotera and Lax equations with forcing term.

New periodic and soliton solutions for the Generalized BBM and Burgers–BBM equations

Abstract In this paper, we consider the Benjamin Bona Mahony equation (BBM), and we obtain new exact solutions for it by using a generalization of the well-known tanh–coth method. New periodic and soliton solutions for the Generalized BBM and Burgers–BBM equations are formally derived.

Special symmetries to standard Riccati equations and applications

By using symmetries associated to Riccati equation in standard form (SRE), we obtain a family which can be integrated by quadratures. As a consequence, we get a new integrability condition for the generalized Riccati equation (GRE). We illustrate the result with some examples and we give some applications in the solitons theory.

The variational iteration method combined with improved generalized tanh–coth method applied to Sawada–Kotera equation

Abstract We obtain new exact solutions to generalized Sawada–Kotera equation. Using the variational iteration method combined with the improved generalized tanh–coth method, we construct new traveling wave solutions for the standard Sawada–Kotera equation and, by means of scaling, we obtain new solutions to general Sawada–Kotera equation. Periodic and soliton solutions are formally derived for both models.