Investigation of the Mathematical Model of Acoustic Waves in a Fluid with Bubbles Using Lie Group Analysis Method

University essay from Blekinge Tekniska Högskola/Sektionen för ingenjörsvetenskap

Abstract:

This thesis comprises investigation of the mathematical model of acoustic waves in a fluid with bubbles for nonlinear self-adjointness, Lie point symmetries, conservation laws and invariant solutions. It is based on the theory developed recently by Prof. Nail Ibragimov. It is shown that the systems of differential equations describing the model are nonlinearly self-adjoint. The symmetries are calculated and the conservation laws are constructed using the formal Lagrangian. In addition, invariant solutions are derived.

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