Tsunami Solitons Emerging from Superconducting Gap

Abstract

We propose a classical integrable system exhibiting tsunami-like solitons with a rocky-desert-like disordered stationary background. One of the Lax operators describing this system is interpretable as a Bogoliubov--de Gennes Hamiltonian in parity-mixed superconductors. The family of integrable equations is generated from this seed operator using Krichever's method, whose pure $s$-wave limit includes the coupled Schrödinger--Boussinesq hierarchy applied to plasma physics. A linearly unstable finite background with a superconducting gap supports the tsunami-soliton solution, where the propagation of the step structure turns back at a certain moment, accompanied with the oscillation on the opposite side. In addition, the equation allows inhomogeneous stationary solutions with an arbitrary number of bumps at arbitrary positions, which we term \textit{the Korteweg--de Vries (KdV) rocks}. In the Zakharov--Shabat scheme, the tsunami solitons are created from the Bogoliubov quasiparticles in the energy gap and the KdV rocks from normal electrons/holes. The unexpected large space of stationary solutions originates from the non-coprime Lax pair and the multivalued Baker--Akhiezer functions on the Riemann surface, formulated in terms of higher-rank holomorphic bundles by Krichever and Novikov. Furthermore, the concept of \textit{isodispersive phases} is introduced to characterize quasiperiodic multi-tsunami backgrounds and consider their classification.

6 pages, 3 figures, 1 table, and ancillary files including 2 gif animations and 5 Mathematica notebooks; v5:a typo fixed. JPSJ Editors' Choice and featured in JPS Hot Topics! Please take a look: https://doi.org/10.7566/JPSHT.6.007

References in corpus (36)

• Nonlinear Schrödinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions
• Fermi gases in one dimension: From Bethe Ansatz to experiments
• Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation
• On Dispersive and Classical Shock Waves in Bose-Einstein Condensates and Gas Dynamics
• On the nonlinear stage of Modulation Instability
• Dynamics of rogue waves in the Davey-Stewartson II equation
• Universal theory of nonlinear Luttinger liquids
• Inhomogeneous Condensates in the Thermodynamics of the Chiral NJL_2 model
• Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems
• Integrable turbulence and formation of rogue waves
• Multi-breathers and high order rogue waves for the nonlinear Schrödinger equation on the elliptic function background
• A Twisted Kink Crystal in the Chiral Gross-Neveu model
• Dark solitons in F=1 spinor Bose--Einstein condensate
• The dynamics of dark solitons in a trapped superfluid Fermi gas
• Phonons, pions and quasi-long-range order in spatially modulated chiral condensates
• Inverse scattering method for square matrix nonlinear Schrödinger equation under nonvanishing boundary conditions
• Exact relaxation dynamics of a localized many-body state in the 1D bose gas
• Dirac-Fermion-Induced Parity Mixing in Superconducting Topological Insulators
• The Bogoliubov/de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry
• Self-consistent multiple complex-kink solutions in Bogoliubov-de Gennes and chiral Gross-Neveu systems
• Parity-Mixed Superconductivity in Locally Non-centrosymmetric System
• Time-Dependent Hartree-Fock Solution of Gross-Neveu models: Twisted Kink Constituents of Baryons and Breathers
• Quantum states of dark solitons in the 1D Bose gas
• Decay of fermionic quasiparticles in one-dimensional quantum liquids
• Imbalanced Superfluid Phase of a Trapped Fermi Gas in the BCS-BEC Crossover Regime
• Fermionic solutions of chiral Gross-Neveu and Bogoliubov-de Gennes systems in nonlinear Schrödinger hierarchy
• Localized structures on librational and rotational travelling waves in the sine-Gordon equation
• Topological Excitations in Spinor Bose-Einstein Condensates
• Integrable model for density-modulated quantum condensates: solitons passing through a soliton lattice
• Full time-dependent Hartree-Fock solution of large N Gross-Neveu models
• Thermodynamics, spin-charge separation and correlation functions of spin-1/2 fermions with repulsive interaction
• Marginally Stable Topologically Non-Trivial Solitons in the Gross-Neveu Model
• Bogoliubov-de Gennes Soliton Dynamics in Unconventional Fermi Superfluids
• On reflectionless nature of self-consistent multi-soliton solutions in Bogoliubov-de Gennes and chiral Gross-Neveu models
• Excitation of the Higgs Mode in a Superfluid Fermi Gas in the BCS-BEC Crossover
• Non-Abelian twisted kinks in chiral Gross-Neveu model with isospin