Solution of the Riemann problem for polarization waves in a two-component Bose-Einstein condensate
arXiv:1709.04193 · doi:10.1103/PhysRevE.96.062202
Abstract
We provide a classification of the possible flow of two-component Bose-Einstein condensates evolving from initially discontinuous profiles. We consider the situation where the dynamics can be reduced to the consideration of a single polarization mode (also denoted as "magnetic excitation") obeying a system of equations equivalent to the Landau-Lifshitz equation for an easy-plane ferro-magnet. We present the full set of one-phase periodic solutions. The corresponding Whitham modulation equations are obtained together with formulas connecting their solutions with the Riemann invariants of the modulation equations. The problem is not genuinely nonlinear, and this results in a non-single-valued mapping of the solutions of the Whitham equations with physical wave patterns as well as to the appearance of new elements --- contact dispersive shock waves --- that are absent in more standard, genuinely nonlinear situations. Our analytic results are confirmed by numerical simulations.
References in corpus (19)
- Spin domains in ground state spinor Bose-Einstein condensates
- The dynamics of component separation in a binary mixture of Bose-Einstein condensates
- Spinor Bose-Einstein condensates
- Dispersive shock waves and modulation theory
- Generation of dark-bright soliton trains in superfluid-superfluid counterflow
- Domain walls of relative phase in two-component Bose-Einstein condensates
- Resolution of a shock in hyperbolic systems modified by weak dispersion
- Undular bore theory for the Gardner equation
- Dispersive and diffusive-dispersive shock waves for nonconvex conservation laws
- Magnetic Solitons in a Binary Bose-Einstein Condensate
- Vector Dark-Antidark Solitary Waves in Multi-Component Bose-Einstein condensates
- Spin-Dipole Oscillation and Polarizability of a Binary Bose-Einstein Condensate near the Miscible-Immiscible Phase Transition
- Breaking of Galilean invariance in the hydrodynamic formulation of ferromagnetic thin films
- Nonlinear waves of polarization in two-component Bose-Einstein condensates
- Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion
- Dispersive hydrodynamics of nonlinear polarization waves in two-component Bose-Einstein condensates
- Riemann problem for the photon fluid: self-steepening effects
- Vortex-antivortex proliferation from an obstacle in thin film ferromagnets
- Expansion Dynamics of a Two-Component Quasi-One-Dimensional Bose-Einstein Condensate: Phase Diagram, Self-Similar Solutions, and Dispersive Shock Waves
Cited by in corpus (14)
- Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point
- Riemann problem for the light pulses in optical fibers for the generalized Chen-Lee-Liu equation
- Riemann problem for the photon fluid: self-steepening effects
- Dynamic soliton-mean flow interaction with nonconvex flux
- Quantum-torque-induced breaking of magnetic interfaces in ultracold gases
- Oscillating Solitons and AC Josephson Effect in Ferromagnetic Bose-Bose Mixtures
- Self-stabilizing exchange-mediated spin transport
- Perspectives on spin hydrodynamics in ferromagnetic materials
- Quasiclassical integrability condition in AKNS scheme
- Simple waves in a two-component Bose-Einstein condensate
- Spin-injection-generated shock waves and solitons in a ferromagnetic thin film: the spin piston problem
- Trigonometric shock waves for the Kaup-Boussinesq system
- Spin-Injection-Generated Shock Waves and Solitons in a Ferromagnetic Thin Film
- Evolution of initial discontinuities in the DNLS equation theory