A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

TL;DR

This paper introduces a new completely integrable (2+1) dimensional evolution equation for ion acoustic waves in magnetized plasmas, extending known models and providing exact solutions and stability analysis.

Contribution

It derives a novel (2+1)D integrable equation for ion acoustic waves, connecting it to known equations and solving it explicitly with soliton and lump solutions.

Findings

Derived exact soliton and lump solutions

Analyzed modulational instability and growth rates

Established mathematical properties confirming integrability

Abstract

A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrodinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bili- nearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathe- matical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the corresponding growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2{\th}1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.