Author(s)

Jennie D’Ambroise¹, Floyd L. Williams²

¹Department of Mathematics/CIS, SUNY Old Westbury, Old Westbury, NY, USA.
²Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, USA.

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.

Cold Plasma, Magnetoacoustic Waves, Resonance Nonlinear Schrödinger Equation, Reaction Diffusion System, Jackiw-Teitelboim Black Hole, Dilaton Field, Ricci Scalar Curvature, Jacobi Elliptic Function

D’Ambroise, J. and Williams, F. (2020) Relating Some Nonlinear Systems to a Cold Plasma Magnetoacoustic System. Journal of Modern Physics, 11, 886-906. doi: 10.4236/jmp.2020.116054.