Solitons and nonlinear waves along quantum vortex filaments under the low-temperature two-dimensional local induction...

Area of Science:

• Condensed Matter Physics
• Quantum Fluids
• Mathematical Physics

Background:

• Experimental evidence confirms Kelvin waves on quantized vortex filaments in superfluid helium.
• Understanding vortex filament dynamics is crucial for superfluid physics.
• Previous work established a 2D Hamiltonian formulation for low-temperature vortex dynamics.

Purpose of the Study:

• To develop a novel analytical approach for 2D vortex filament dynamics.
• To derive new solutions for the 2D Local Induction Approximation (LIA).
• To connect LIA with integrable systems for systematic solution generation.

Main Methods:

• Establishing a correspondence between the 2D LIA and the Wadati-Konno-Ichikawa-Schimizu (WKIS) hierarchy.
• Deriving solutions (helix, planar, self-similar) directly from the WKIS equation.
• Coupling the approach with inverse scattering transform methods for solitary wave solutions.

Main Results:

• New analytical solutions for the 2D LIA were obtained efficiently.
• The method allows direct derivation of vortex filament solutions in Cartesian coordinates.
• Solitary wave solutions, including a Hasimoto soliton analog, were found.

Conclusions:

• The WKIS hierarchy provides a powerful framework for analyzing 2D vortex filament dynamics.
• This approach simplifies the study of Kelvin waves and solitary waves in superfluids.
• The findings have implications for understanding post-vortex reconnection events and experimental observations.