# Standing waves in a counter-rotating vortex filament pair

## TL;DR

This paper investigates standing wave solutions in a model of counter-rotating vortex filaments, revealing an infinite bifurcation of periodic standing waves from a basic steady configuration.

## Contribution

It introduces a bifurcation analysis showing the existence of infinitely many periodic standing wave solutions in the vortex filament model.

## Key findings

- Existence of multiple bifurcating branches of standing waves.
- Periodic solutions with rational frequencies.
- Analytical characterization of wave patterns.

## Abstract

The distance among two counter-rotating vortex filaments satisfies a beam-type of equation according to the model derived in [15]. This equation has an explicit solution where two straight filaments travel with constant speed at a constant distance. The boundary condition of the filaments is 2${\pi}$-periodic. Using the distance of the filaments as bifurcating parameter, an infinite number of branches of periodic standing waves bifurcate from this initial configuration with constant rational frequency along each branch.