J. C. Camacho

• Universidad de Cádiz

This work investigates a spatially two-dimensional advection–diffusion–reaction equation that generalizes the Burgers’ and the Fisher's equations, having the properties of convective phenomenon from Burgers equation as well as diffusion transport and reaction phenomena from Fisher's equation. The two-dimensional equation is analysed from the point...

Nonlinear partial differential equations are used to describe complex phenomena in various fields of science. In this work, we consider a generalized fourth‐order nonlinear wave equation from the point of view of the theory of symmetry reductions in partial differential equations. We derive classical symmetries, and we obtain the reductions from th...

In this work we study the classical Lie symmetries and the consevations laws of a generalized Dullin-Gottwald-Holm equation with arbitrary coefficients.

In this paper we consider a generalized Fornberg-Whitham Equation. We make an analysis of the symmetries of this equation by using the classical Lie symmetry method. Symmetry reductions are derived from an optimal system of subalgebras and lead to ordinary differential equations. We obtain travelling wave solutions. In addition, by using the genera...

In this work, we consider a generalized Fisher equation and we have considered this equation from the point of view of the theory of symmetry reductions in partial differential equations. Generalizations of the Fisher equation are needed to more accutarely model complex diffusion and reactions effects found in many biological systems. The reduction...

We determine symmetry reductions of a Generalized Dullin-Gottwald-Holm equation. We obtain the subclasses of these general equations which are quasi self-adjoint and weak self-adjoint.

In this paper we make a full analysis of the symmetry reductions of a beam equation by using the classical Lie method of infinitesimals and the nonclassical method. We consider travelling wave reductions depending on the form of an arbitrary function. We have found several new classes of solutions that have not been considered before: solutions exp...

In this paper, the family of BBM equation with strong nonlinear dispersive B(m, n) is con-sidered. We apply the classical Lie method of infinitesimals. The symmetry reductions are derived from the optimal system of subalgebras and lead to systems of ordinary differential equations. We obtain for special values of the parameters of this equation, ma...

In this paper we find exact solutions for a beam equation. We make a full analysis of the symmetry reductions of this equation by using the classical Lie method of infinitesimals. We present some explicit solutions: compacton solutions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We apply the Lie-group formalism and the nonclassical method due to Bluman and Cole to deduce symmetries of the generalized Kuramoto–Sivashinsky equation with dispersive effects. We make a full analysis of the symmetry reductions and we prove that the nonclassical method applied to the equation leads to new reductions, which cannot be obtained by L...

Resumen En este trabajo presentamos un estudio, desde el punto de vista de la teoría de las simetrías potenciales clásicas y no clásicas para ecuaciones en derivadas parciales, del modelo que describe las vibraciones de una viga.