Estudo de ondas viajantes não lineares de perfil saturado

Abstract

In this paper, we study a class of nonlinear waves in one dimension using the assumption of traveling waves. First we found the solutions to the partial differential equation (PDE) containing a term of nonlinear inhomogeneity, rø (1-øl), which conditions the wave to present a saturation profile. We found analytical solutions for specific cases and also we transformed the partial differential equation in integral form, studying the solutions. In possession of the solutions, a study of the parameters' variation according to the value of the exponent l of the equation's nonlinear term was conducted. We also make an approach to the problem with the Lagrangian and Hamiltonian functions, making it possible to define the wave's energy. In the last part of this paper we write the EDP in the discrete form of finite difference. We solved the equation numerically and studied l = 1; 2 and varying the parameter that multiplies the inhomogeneous term. We found that the solution can go from a regular saturated profile to chaotic behavior.