M. Rosa

Symmetries and Conservation Laws for Some Compacton Equation

We consider some equations with compacton solutions and nonlinear dispersion from the point of view of Lie classical reductions. The reduced ordinary differential equations are suitable for qualitative analysis and their dynamical behaviour is described. We derive by using the multipliers method some nontrivial conservation laws for these equations.

Classical and potential symmetries for a generalized Fisher equation

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 accurately model complex diffusion and reaction effects found in many biological systems. The reductions to ordinary differential equations are derived from the optimal system of subalgebras and new exact solutions are obtained. The potential system has been achieved from the complete list of the conservation laws. Potential symmetries, which are not local symmetries, are carried out for the generalized Fisher equation, these symmetries lead to the linearization of the equation by non-invertible mappings.

A conservation law for a generalized chemical Fisher equation

In this work we study a generalized Fisher equation with variable coefficients from the point of view of the theory of symmetry reductions in partial differential equations. There is a widespread occurrence of nonlinear phenomena in physics, chemistry and biology. This clearly necessitates a study of conservation laws in depth and of the modeling and analysis involved. We determine the class of these equations which are nonlinearly self-adjoint. By using a general theorem on conservation laws proved by Nail Ibragimov and the symmetry generators we find some conservation laws for some of these partial differential equations without classical Lagrangians.

Conservation laws for a strongly damped wave equation

Abstract A strongly damped wave equation including the displacement depending nonlinear damping term and nonlinear interaction function is considered. Classical symmetries, exact solutions and conservation laws are derived.

Symmetries and conservation laws of a damped Boussinesq equation

In this work, we consider a damped equation with a time-independent source term. We derive the classical Lie symmetries admitted by the equation as well as the reduced ordinary differential equations. We also present some exact solutions. Conservation laws for this equation are constructed by using the multiplier method.

Classical symmetries, travelling wave solutions and conservation laws of a generalized Fornberg-Whitham equation

In this paper, we consider a generalized Fornberg-Whitham Equation. We make an analysis of the symmetries of this equation 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, using the general multiplier method, new conservation laws of this equation are determined.

On Symmetries and Conservation Laws for a Generalized Fisher–Kolmogorov–Petrovsky–Piskunov Equation

This chapter presents a generalized Fisher equation (GFE) from the point of view of the theory of symmetry reductions in partial differential equations. The GFE can be used to describe an ideal growth and spatial-diffusion phenomena. The reductions to ordinary differential equations are derived from the optimal system of subalgebras and new exact solutions are obtained. Conservation laws for this equation are constructed. The potential system has been achieved from the complete list of the conservation laws. Potential symmetries, which are not local symmetries, are carried out for the generalized Fisher equation, these symmetries lead to the linearization of the equation by non-invertible mappings.

Conservation laws and symmetries of a generalized Kawahara equation

The generalized Kawahara equation ut = a(t)uxxxxx + b(t)uxxx + c(t) f (u)ux appears in many physical applications. A complete classification of low-order conservation laws and point symmetries is obtained for this equation, which includes as a special case the usual Kawahara equation ut = αuux + βu2ux + γuxxx + μuxxxxx. A general connection between conservation laws and symmetries for the generalized Kawahara equation is derived through the Hamiltonian structure of this equation and its relationship to Noether’s theorem using a potential formulation.

On conservation laws for a generalized Boussinesq equation

In this work, we study a Boussinesq equation with a strong damping term from the point of view of the Lie theory. By using the low order conservation laws we apply the conservation laws multiplier method to the associated potential systems.In this work, we study a Boussinesq equation with a strong damping term from the point of view of the Lie theory. By using the low order conservation laws we apply the conservation laws multiplier method to the associated potential systems.

Symmetries and nonlinear self-adjointness for a generalized fisher equation

In this work we study a generalization of the well known Fisher equation from the point of view of the theory of symmetry reductions in partial differential equations. We determine the class of these equations which are nonlinear self-adjoint. By using a general theorem on conservation laws proved by Nail Ibragimov we find conservation laws for some of these partial differential equations without classical Lagrangians.