29 papers
This paper investigates the motion of compressible, inviscid fluid on a rotating sphere by presenting hodograph equations that yield a class of solutions parameterized by two arbitrary functions, providing explicit examples, describing blow-up curves, and analyzing limiting cases of rotation speeds.
This paper investigates three eigenfunction constraints on the differential-difference Kadomtsev-Petviashvili (DKP) hierarchy, demonstrating that a squared eigenfunction constraint yields the semi-discrete AKNS hierarchy while two distinct linear eigenfunction constraints lead to a combined semi-discrete Burgers hierarchy, with all results rigorously proved using recursive algebraic structures generated by master symmetries.
This paper demonstrates that the Poisson algebras of cohomological and -theoretic Coulomb branches in 3d necklace quiver gauge theories reproduce the equations of motion for rational and hyperbolic spin Ruijsenaars-Schneider models, respectively, while explicitly revealing their underlying affine Yangian and quantum toroidal superintegrability structures.
This paper establishes that the classical Darboux system admits a scalar Lagrangian formulation equivalent to the generating PDE of the KP hierarchy, extends this framework to differential-difference and fully discrete versions using elementary and special functions respectively, and demonstrates that their dispersionless limits yield a complete classification of 3D second-order integrable Lagrangians.
This paper demonstrates that the saddle-point configuration for thermal phase slips in an infinite superconducting film near the critical current is exactly solvable via the Boussinesq equation, revealing specific scaling laws for the instanton size and activation energy that explain the behavior of superconducting strips used in photon detection.
This paper classifies low-order local Hamiltonian operators for two-component evolutionary differential-difference equations, including degenerate cases beyond previous scalar results, and computes the Poisson cohomology of a specific degenerate operator to elucidate its deformation theory and bi-Hamiltonian structure in integrable systems like the Toda lattice.
This paper introduces new "vertical" intertwining operators that change the particle number in the quantum Calogero model for integer coupling, complementing existing "horizontal" operators to form a grid structure that enables the derivation of Liouville charges and a new basis of non-symmetric integrals through iterated intertwining.
This review paper demonstrates that six specific two-dimensional quantum superintegrable systems in flat space are exactly solvable and share a common hidden Lie algebraic structure, characterized by polynomial eigenfunctions, infinite flags of invariant subspaces, and finite-order polynomial algebras of integrals.
This paper investigates the blowup phenomena of Toda systems, which generalize the Liouville equation via simple Lie algebras, by providing concrete examples of blowup masses that correspond to Weyl groups.