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Integrable (3 + 1)-Dimensional Generalization for the Dispersionless Davey–Stewartson System
This paper introduces a (3 + 1)-dimensional dispersionless integrable system, utilizing a Lax pair involving contact vector fields, in alignment with...
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Brick wall diagrams as a completely integrable system
We study the free energy of an integrable, planar, chiral and non-unitary four-dimensional Yukawa theory, the bi-fermion fishnet theory discovered by...
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A nonlocal finite-dimensional integrable system related to the nonlocal mKdV equation
AbstractWe propose a hierarchy of the nonlocal mKdV (NmKdV) equation. Based on a constraint, we obtain nonlocal finite-dimensional integrable...
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Summability of Transseries Solution of Non-integrable Hamiltonian System
This paper studies the summability of the transseries solution of a nonintegrable Hamiltonian system. Since our system has a resonance and is not...
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Thermalization and Hydrodynamics in an Interacting Integrable System: The Case of Hard Rods
We consider the relaxation of an initial non-equilibrium state in a one-dimensional fluid of hard rods. Since it is an interacting integrable system,...
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Eight Lectures on Integrable Systems
These lectures provide an introduction to the theory of integrable systems from the point of view of Poisson manifolds. In classical mechanics, an...
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Experimental verification of generalized eigenstate thermalization hypothesis in an integrable system
Identifying the general mechanics behind the equilibration of a complex isolated quantum system towards a state described by only a few parameters...
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Quantum and Classical Integrable Systems
The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the...
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Fractional Integrable Dispersive Equations
Fractional equations arise widely in physical systems and nonlinear integrable systems are fundamentally important in the study of nonlinear...
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Polygon recutting as a cluster integrable system
Recutting is an operation on planar polygons defined by cutting a polygon along a diagonal to remove a triangle, and then reattaching the triangle...
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Integrable Systems Related to Matrix LR Transformations
The discrete Toda (dToda) equation, which is a representative integrable system, is the recursion formula of the well-known quotient-difference...
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From one to infinity: symmetries of integrable systems
Integrable systems constitute an essential part of modern physics. Traditionally, to approve a model is integrable one has to find its infinitely...
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Quasi-Integrable Modules over Twisted Affine Lie Superalgebras
In this paper, we characterize quasi-integrable modules, of nonzero level, over twisted affine Lie superalgebras. We show that these form a class of...
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Dualities in quantum integrable many-body systems and integrable probabilities. Part I
In this study we map the dualities observed in the framework of integrable probabilities into the dualities familiar in a realm of integrable...
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Integrable Mechanical Billiards in Higher-Dimensional Space Forms
In this article, we consider mechanical billiard systems defined with Lagrange’s integrable extension of Euler’s two-center problems in the Euclidean...
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On Differential Equations of Integrable Billiard Tables
We introduce a method to find differential equations for functions which define tables, such that associated billiard systems admit a local first...
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New Completely Integrable Dispersionless Dynamical System of Heavenly Type Generated By Vector Fields on a Torus
We study the problem of construction of a new spatially two-dimensional and dispersionless Lax–Sato completely integrable heavenly type equation.
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Solvable Algebras and Integrable Systems
This paper discusses a range of questions concerning the application of solvable Lie algebras of vector fields to exact integration of systems of...