Solitonlike solutions of magnetostatic equilibria: Plane-symmetric case

TL;DR

This paper demonstrates the existence of solitonlike solutions to the nonlinear Grad-Shafranov equation in a plane-symmetric setting, providing a basis for modeling astrophysical jets with knotty structures.

Contribution

It introduces a numerical method to find and analyze solitonlike solutions of the magnetostatic equilibrium equations, confirming their existence despite instability issues.

Findings

Solitonlike solutions exist in plane-symmetric magnetostatic equilibria.

The solutions exhibit soliton and periodic structures in different directions.

The method enables future studies of axisymmetric solutions for astrophysical applications.

Abstract

We present the plane-symmetric solitonlike solutions of magnetostatic equilibria by solving the nonlinear Grad-Shafranov (GS) equation numerically. The solutions have solitonlike and periodic structures in the $x$ and $y$ directions, respectively, and $z$ is the direction of plane symmetry. Although such solutions are unstable against the numerical iteration, we give the procedure to realize the sufficient convergence. Our result provides the definite answer for the existence of the solitonlike solutions that was questioned in recent years. The method developed in this paper will make it possible to study the axisymmetric solitonlike solutions of the nonlinear GS equation, which could model astrophysical jets with knotty structures.