TITLE:
Relating Some Nonlinear Systems to a Cold Plasma Magnetoacoustic System
AUTHORS:
Jennie D’Ambroise, Floyd L. Williams
KEYWORDS:
Cold Plasma, Magnetoacoustic Waves, Resonance Nonlinear Schrödinger Equation, Reaction Diffusion System, Jackiw-Teitelboim Black Hole, Dilaton Field, Ricci Scalar Curvature, Jacobi Elliptic Function
JOURNAL NAME:
Journal of Modern Physics,
Vol.11 No.6,
June
5,
2020
ABSTRACT: Using a Gurevich-Krylov solution that describes the propagation of nonlinear magnetoacoustic waves in a cold plasma, we construct solutions of various other nonlinear systems. These include, for example, Madelung fluid, reaction diffusion, Broer-Kaup, Boussinesq, and Hamilton-Jacobi-Bellman systems. We also construct dilaton field solutions for a Jackiw-Teitelboim black hole with a negative cosmological constant. The black hole metric corresponds to a cold plasma metric by way of a change of variables, and the plasma dilatons and cosmological constant also have an expression in terms of parameters occurring in the Gurevich-Krylov solution. A dispersion relation, moreover, links the magnetoacoustic system and a resonance nonlinear Schrödinger equation.