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 Schrodinger equation.
Highlights
Over the past years, points of connection of plasma physics to various nonlinear equations of significant importance have been explored
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
In addition to the solutions (11), (14) of the Madelung fluid and RD systems (4), (12), and the resonance nonlinear Schrödinger (RNLS) solution (15) of (1), all of which were constructed by way of the Gurevich and A. Krylov (G-K) solution (10), we consider solutions of nonlinear systems of Broer-Kaup (B-K), Boussinesq, and Hamilton-Jacobi-Bellman (H-J-B), and of their time reversal ( t → −t ) systems
Summary
Points of connection of plasma physics to various nonlinear equations of significant importance have been explored. The velocity field u of the plasma is given by u = −2Sx. In the present paper we consider for an arbitrary γ < 0 solutions of Equation (1) of the form ψ = eR−iS (3). The main result of that section is the computation of two more plasma dilaton fields such that these combined with the one computed in [10] form a linearly independent set This too generalizes in a non-trivial way (namely the case α1 ≠ 0 ) a result found in [12]. In addition to the solutions (11), (14) of the Madelung fluid and RD systems (4), (12), and the RNLS solution (15) of (1), all of which were constructed by way of the G-K solution (10), we consider solutions of nonlinear systems of Broer-Kaup (B-K), Boussinesq, and Hamilton-Jacobi-Bellman (H-J-B), and of their time reversal ( t → −t ) systems. Again, the G-K solution (10) of the MAS (5) plays an underlying, subtextual role
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