Simetrías de Lie y leyes de conservación en ecuaciones de evolución no lineales.

Abstract

Trade laws play an important role in science and engineering. The goal of this thesis is to provide a review and application of the latest methods for constructing conservation laws using Lie group theory. Classically the derivation of conservation laws for invariant variational problems is based on Noether¿s theorem. However N. H. ibragimov proposes a new conservation theorem which applies to EDP or EDP systems without Lagrangians. The Kudryashov-Sinelshchikov equation describes the phenomena of pressure waves in mixtures of liquid-gas bubbles under the consideration of heat transfer and viscosity. In this investigation we discuss how to find conservation laws to the aforementioned equation, we will use a recent version of Noether¿s Theorem which is based on the concept of an attached equation for an EDP or EDP system and the introduction of a formal Lagrangian. Specifically we will find the attached of the equation Kudryashov- Sinelshchikov. For this we have to know its infinitesimal generators (which will be those that provide us with the symmetries of our equation), and the generalized associated Euler-Lagrange operator, to later be able to calculate its conservation laws using N. Ibragimov¿s theorem.