Nonlinear ion acoustic waves scattered by vortexes

TL;DR

This paper introduces a modified KP model incorporating vortex effects, revealing how vortexes scatter ion acoustic waves, break integrability, and induce chaotic behavior in soliton dynamics.

Contribution

It extends the classical KP hierarchy by adding vortex terms, creating a new model for wave-vortex interactions in plasma physics.

Findings

Vortexes cause scattering and chaos in ion acoustic solitons.

The vortex term breaks the integrability of the KP system.

Numerical simulations demonstrate wave scattering by vortexes.

Abstract

The Kadomtsev--Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes `scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are `ambient' because they do not receive reciprocal reactions from the waves (i.e., the vortex equation is independent of the wave fields). This model describes a minimal departure from the integrable KP system. By the Painlev\'e test, we delineate how the vorticity term violates integrability, bringing about an essential three-dimensionality to the solutions. By numerical simulation, we show how the solitons are scattered by vortexes and become chaotic.