Gardner, C.S. and Morikawa, G.K. (1960) Similarity in the Asymptotic Behavior of Collision-Free Hydromagnetic Waves and Water Waves. Courant Institute of Mathematical Sciences Report No. NYO 9082 (Unpublished).

has been cited by the following article:

• 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.