Soliton gas in bidirectional dispersive hydrodynamics

Area of Science:

• Physics
• Fluid Dynamics
• Nonlinear Systems

Background:

• Soliton gas theory was previously limited to unidirectional systems.
• Soliton properties were determined by elastic pairwise interactions.
• Bidirectional interactions were not previously considered.

Purpose of the Study:

• Extend soliton gas theory to bidirectional integrable Eulerian systems.
• Investigate the behavior of soliton gases with both head-on and overtaking collisions.
• Develop kinetic equations and solve shock-tube problems for these systems.

Main Methods:

• Distinguished between isotropic and anisotropic bidirectional soliton gases based on collision-induced position shifts.
• Constructed kinetic equations for both types of gases.
• Solved shock-tube problems using weak solutions of the kinetic equations.
• Validated analytical results with direct numerical simulations.

Main Results:

• Developed a theory for bidirectional soliton gases, classifying them as isotropic or anisotropic.
• Derived kinetic equations and obtained analytical solutions for shock-tube Riemann problems.
• Demonstrated the equivalence of the resonant nonlinear Schrödinger (NLS) equation soliton gas kinetic equation to that of the Kaup-Boussinesq shallow-water system.
• Showed excellent agreement between analytical predictions and numerical simulations.

Conclusions:

• The extended theory accurately describes bidirectional soliton gases.
• Kinetic equations provide a powerful tool for analyzing these complex systems.
• The findings have implications for understanding nonlinear wave phenomena in various physical contexts.