29 papers
This paper constructs modular families of quantum-integrable elliptic long-range spin chains with q-deformed interactions by freezing spin-Ruijsenaars systems at classical equilibrium configurations, thereby providing a unified framework that interpolates between nearest-neighbour and long-range models while encompassing various known integrable chains and their deformations.
This paper revisits quadratic Bureau-Guillot systems containing first and second Painlevé transcendent coefficients, utilizing Okamoto's geometric approach and iterative polynomial regularisation to establish their birational equivalence, resolve the Painlevé equivalence problem for non-rational meromorphic coefficients, and identify a Hamiltonian formulation for one of the systems.
This paper provides an informal introduction to the integrable systems approach to the Schottky problem, detailing how Jacobian theta functions yield solutions to the KP equation and culminating in Krichever's proof of Welters' trisecant conjecture for the most degenerate flex line case.
This paper investigates the weak-coupling limit of the lattice nonlinear Schrödinger integral equation by employing matched asymptotic expansions to derive the ground-state energy and density, revealing a logarithmic divergence linked to the Bose-Einstein distribution and uncovering a resurgent transseries structure through Wiener-Hopf analysis.
This paper reviews and contrasts the long-time behavior of initial-boundary value problems for systems admitting Lax Pair formulations, illustrating cases where integrability ensures regular asymptotic behavior alongside instances where irregular, fractal-like chaos emerges, while connecting these findings to perturbed Lax Pair theory on the real line.
This paper demonstrates that for a specific class of state integral models on shaped pseudo 3-manifolds, including the edge formulation of Teichmüller TQFT, the Boltzmann weight assigned to a tetrahedron satisfies the tetrahedron equation, with the tetrahedron's dihedral angles serving as spectral parameters.
This paper constructs a novel family of exact cnoidal waves and dark solitons for the focusing and defocusing Ablowitz-Ladik equations, characterized by a "swinging" phase with nonlinear dependence on time and site number, derived via a two-point map that enables arbitrary lattice positioning and establishes explicit velocity quantization rules for waves on closed loops.
This paper analyzes the phase-space features of a Toda-like Hamiltonian constrained by specific conditions to demonstrate that it not only analytically reproduces classical Lotka-Volterra prey-predator dynamics but also exhibits quantum stability through non-perturbative distortions, thereby establishing a predictive framework for quantized competitive biosystems.
This paper establishes global well-posedness in the critical energy space and proves almost periodicity in time for the half-wave maps equation on the one-dimensional torus by leveraging its integrable Lax pair structure to derive explicit solution formulae and a general stability principle that extends to matrix-valued cases and companion results on the real line.
This paper derives general bright-dark soliton solutions to the coupled Sasa-Satsuma equation under mixed boundary conditions by constructing two-bright-two-dark solutions for the four-component Hirota equation via the KP reduction method and analyzing their dynamical behaviors.
This paper presents a simple construction of algebro-geometric solutions to the Gelfand–Dickey hierarchy using an -type infinite ODE system and Dubrovin's method, while also deriving a formula for the -point function of the associated Riemann -function.
This paper establishes the integrability of a one-parameter family of coupled Dirac-scalar field theories in dimensions that interpolates between the Dirac-sinh-Gordon and Dirac-sine-Gordon systems by constructing an explicit -valued Lax pair, proving the physical non-triviality of the deformation, and deriving associated conserved densities.
This paper presents an English translation and digitization of Sophie Kowalevski's 1889 French publication on the rotation of a rigid body about a fixed point, which introduced the famous Kovalevskaya Top.
This paper refutes the "all-or-nothing" expectation for local commuting charges in non-Hermitian bosonic chains by constructing explicit counterexamples with selective k-local charges, thereby demonstrating the limited universality of the Grabowski–Mathieu integrability test and providing a complete classification of such models.
This paper introduces a symmetry-resolved framework that decomposes high-dimensional Liouvillian dynamics into low-dimensional invariant sectors to systematically identify and characterize exceptional points in realistic open quantum systems, accompanied by a numerical diagnostic metric for quantifying their proximity.
This paper investigates the geometric, algebraic, and analytic properties of hyperelliptic functions as a generalization of Jacobi elliptic functions and demonstrates their role as potential solutions to the nonlinear Schrödinger and complex modified Korteweg-de Vries equations.
This paper extends the framework of invariant reduction for partial differential equations to handle geometric structures that are rescaled rather than strictly invariant by symmetries, establishing a shift rule that explains the emergence or loss of invariance in reduced systems and enabling the geometric construction of exact solutions without relying on integrability structures like Lax pairs.
This paper provides an explicit description of the phase space stratification for Calogero-Moser-Sutherland systems associated with , demonstrating that each positive-dimensional symplectic stratum is symplectomorphic to and admits natural action-angle coordinates.
This paper proves that for the standard triangle polygon (corresponding to the toric surface ), the spectral transform establishes a birational isomorphism between the Goncharov-Kenyon cluster integrable system and the Beauville integrable system by showing that it intertwines their respective Poisson structures, thereby demonstrating that Beauville integrable systems admit cluster algebra structures.
The paper proves that the height function of the six-vertex model on with spectral parameter converges to a full-plane Gaussian free field in the scaling limit, a result that extends to anisotropic weights via a suitable lattice embedding.