1988, Encyclopaedia of mathematical sciences, ISBN 3540170014, Volume 1-2, <6, 16, 39, 66 >, v. <1-9; in 10 >

Book

Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, 4/2015, Volume 112, Issue 14, pp. 4208 - 4213

We study the original -Fermi–Pasta–Ulam (FPU) system with = 16, 32, and 64 masses connected by a nonlinear quadratic spring. Our approach is based on resonant...

Wave-wave interactions | α-Fermi-Pasta-Ulam chain | FPU recurrence | Resonant interactions | Thermalization | CHAIN | resonant interactions | HAMILTONIAN-SYSTEMS | MULTIDISCIPLINARY SCIENCES | alpha-Fermi-Pasta-Ulam chain | wave-wave interactions | SURFACE | thermalization | LIMIT | EQUIPARTITION | wave–wave interactions | Physical Sciences | α-Fermi–Pasta–Ulam chain

Wave-wave interactions | α-Fermi-Pasta-Ulam chain | FPU recurrence | Resonant interactions | Thermalization | CHAIN | resonant interactions | HAMILTONIAN-SYSTEMS | MULTIDISCIPLINARY SCIENCES | alpha-Fermi-Pasta-Ulam chain | wave-wave interactions | SURFACE | thermalization | LIMIT | EQUIPARTITION | wave–wave interactions | Physical Sciences | α-Fermi–Pasta–Ulam chain

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 2/2018, Volume 91, Issue 3, pp. 1677 - 1680

The search for new integrable $$(3+1)$$ (3+1) -dimensional partial differential systems is among the most important challenges in the modern integrability...

Engineering | Vibration, Dynamical Systems, Control | Classical Mechanics | Contact Lax pairs | Automotive Engineering | Mechanical Engineering | Multidimensional integrable systems | Dispersionless systems | MECHANICS | SOLITONS | ENGINEERING, MECHANICAL | Rational functions

Engineering | Vibration, Dynamical Systems, Control | Classical Mechanics | Contact Lax pairs | Automotive Engineering | Mechanical Engineering | Multidimensional integrable systems | Dispersionless systems | MECHANICS | SOLITONS | ENGINEERING, MECHANICAL | Rational functions

Journal Article

Physics Letters A, ISSN 0375-9601, 2008, Volume 372, Issue 48, pp. 7129 - 7132

The interest in the Camassa–Holm equation inspired the search for various generalizations of this equation with interesting properties and applications. In...

BREAKING | TRAVELING-WAVE SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | STABILITY | TRAJECTORIES | DYNAMICS | PEAKED SOLITONS | EQUATION | Physics - Exactly Solvable and Integrable Systems | Mathematics | Naturvetenskap | Natural Sciences | Matematik

BREAKING | TRAVELING-WAVE SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | STABILITY | TRAJECTORIES | DYNAMICS | PEAKED SOLITONS | EQUATION | Physics - Exactly Solvable and Integrable Systems | Mathematics | Naturvetenskap | Natural Sciences | Matematik

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 03/2011, Volume 44, Issue 10, pp. 103001 - 146

T- and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to...

DIFFERENCE L OPERATORS | CONFORMAL FIELD-THEORY | MOBIUS-INVERSION FORMULA | PHYSICS, MULTIDISCIPLINARY | QUANTUM AFFINE ALGEBRAS | FUNCTIONAL DILOGARITHM IDENTITIES | SOLVABLE LATTICE MODELS | FINITE-DIMENSIONAL REPRESENTATIONS | CLUSTER ALGEBRAS | PHYSICS, MATHEMATICAL | THERMODYNAMIC BETHE-ANSATZ | FACTORIZED S-MATRIX | Algebra | Mathematical analysis | Ideal gas | Field theory | Mathematical models | Schroedinger equation | Statistics | Combinatorial analysis

DIFFERENCE L OPERATORS | CONFORMAL FIELD-THEORY | MOBIUS-INVERSION FORMULA | PHYSICS, MULTIDISCIPLINARY | QUANTUM AFFINE ALGEBRAS | FUNCTIONAL DILOGARITHM IDENTITIES | SOLVABLE LATTICE MODELS | FINITE-DIMENSIONAL REPRESENTATIONS | CLUSTER ALGEBRAS | PHYSICS, MATHEMATICAL | THERMODYNAMIC BETHE-ANSATZ | FACTORIZED S-MATRIX | Algebra | Mathematical analysis | Ideal gas | Field theory | Mathematical models | Schroedinger equation | Statistics | Combinatorial analysis

Journal Article

Physical Review Letters, ISSN 0031-9007, 2019, Volume 122, Issue 4, p. 043901

It is known that the Manakov equation which describes wave propagation in two mode optical fibers, photorefractive materials, etc., can admit solitons which...

FIBERS | STATES | WAVES | SHAPE | PHYSICS, MULTIDISCIPLINARY | PARTIALLY COHERENT SOLITONS | STABILITY | DISSIPATIVE SOLITONS | SPATIAL SOLITONS | PULSES | BRIGHT | Optical fibers | Wave propagation | Wavelengths | Photorefractivity | Solitary waves | Collision dynamics | Propagation modes

FIBERS | STATES | WAVES | SHAPE | PHYSICS, MULTIDISCIPLINARY | PARTIALLY COHERENT SOLITONS | STABILITY | DISSIPATIVE SOLITONS | SPATIAL SOLITONS | PULSES | BRIGHT | Optical fibers | Wave propagation | Wavelengths | Photorefractivity | Solitary waves | Collision dynamics | Propagation modes

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 3/2017, Volume 2017, Issue 3, pp. 1 - 29

We investigate the integrable aspects of the planar γ-deformed ABJM theory and propose the twisted asymptotic Bethe ansatz equations. A more general method...

Integrable Field Theories | AdS-CFT Correspondence | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | STRINGS | INTEGRABLE SPIN CHAIN | TBA | ADS X CP3 | DEFORMATIONS | CHERN-SIMONS | ADS/CFT INTEGRABILITY | PHYSICS, PARTICLES & FIELDS | Mathematical analysis | Asymptotic methods | Physics - High Energy Physics - Theory

Integrable Field Theories | AdS-CFT Correspondence | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | STRINGS | INTEGRABLE SPIN CHAIN | TBA | ADS X CP3 | DEFORMATIONS | CHERN-SIMONS | ADS/CFT INTEGRABILITY | PHYSICS, PARTICLES & FIELDS | Mathematical analysis | Asymptotic methods | Physics - High Energy Physics - Theory

Journal Article

8.
Full Text
The U(n) Gelfand-Zeitlin system as a tropical limit of Ginzburg-Weinstein diffeomorphisms

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-503X, 10/2018, Volume 376, Issue 2131, p. 20170428

In this paper, we show that the Ginzburg-Weinstein diffeomorphism u(n)* -> U(n)* of Alekseev & Meinrenken (Alekseev, Meinrenken 2007 J. Differential Geom. 76,...

Integrable systems | Gelfand-Zeitlin | Tropicalization | Poisson geometry | Poisson-Lie groups | LIE-GROUPS | tropicalization | POISSON | MULTIDISCIPLINARY SCIENCES | TORIC DEGENERATIONS | integrable systems | Mathematics - Symplectic Geometry | 1008 | 112 | Gelfand–Zeitlin | Poisson–Lie groups

Integrable systems | Gelfand-Zeitlin | Tropicalization | Poisson geometry | Poisson-Lie groups | LIE-GROUPS | tropicalization | POISSON | MULTIDISCIPLINARY SCIENCES | TORIC DEGENERATIONS | integrable systems | Mathematics - Symplectic Geometry | 1008 | 112 | Gelfand–Zeitlin | Poisson–Lie groups

Journal Article

Physics Letters A, ISSN 0375-9601, 2008, Volume 372, Issue 15, pp. 2634 - 2639

K 2 S 2 T [A. Karasu-Kalkani, A. Karasu, A. Sakovich, S. Sakovich, R. Turhan, nlin/0708.3247] recently derived a new 6th-order wave equation KdV6: ( ∂ x 2 + 8...

PHYSICS, MULTIDISCIPLINARY | Physics - Exactly Solvable and Integrable Systems

PHYSICS, MULTIDISCIPLINARY | Physics - Exactly Solvable and Integrable Systems

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 2/2018, Volume 108, Issue 2, pp. 359 - 376

We introduce a novel systematic construction for integrable ( $$3+1$$ 3 + 1 )-dimensional dispersionless systems using nonisospectral Lax pairs that involve...

Contact bracket | 37K05 | Theoretical, Mathematical and Computational Physics | Complex Systems | 53D10 | Physics | Dispersionless systems | 37K10 | Geometry | Conservation laws | ( $$3+1$$ 3 + 1 )-Dimensional integrable systems | Contact Lax pairs | Group Theory and Generalizations | (3 + 1)-Dimensional integrable systems | (3+1)-Dimensional integrable systems | CONSERVED-DENSITIES | EQUATIONS | CLASSIFICATION | HIERARCHIES | PHYSICS, MATHEMATICAL | TIME-DEPENDENT SYMMETRIES | Environmental law

Contact bracket | 37K05 | Theoretical, Mathematical and Computational Physics | Complex Systems | 53D10 | Physics | Dispersionless systems | 37K10 | Geometry | Conservation laws | ( $$3+1$$ 3 + 1 )-Dimensional integrable systems | Contact Lax pairs | Group Theory and Generalizations | (3 + 1)-Dimensional integrable systems | (3+1)-Dimensional integrable systems | CONSERVED-DENSITIES | EQUATIONS | CLASSIFICATION | HIERARCHIES | PHYSICS, MATHEMATICAL | TIME-DEPENDENT SYMMETRIES | Environmental law

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 10/2017, Volume 355, Issue 2, pp. 741 - 766

We present a linear system of difference equations whose entries are expressed in terms of theta functions. This linear system is singular at $${4m+12}$$ 4 m +...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | DIFFERENTIAL-EQUATIONS | 2ND-ORDER | PHYSICS, MATHEMATICAL | GEOMETRY

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | DIFFERENTIAL-EQUATIONS | 2ND-ORDER | PHYSICS, MATHEMATICAL | GEOMETRY

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 12/2016, Volume 2016, Issue 12, pp. 1 - 121

We propose an efficient grassmannian formalism for solution of bi-linear finite-difference Hirota equation (T-system) on T-shaped lattices related to the space...

Integrable Field Theories | Supersymmetric gauge theory | AdS-CFT Correspondence | Quantum Physics | Bethe Ansatz | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | Super-symmetric gauge theory | FUNCTIONAL-EQUATIONS | ANALYTIC BETHE-ANSATZ | BAXTERS Q-OPERATORS | CONFORMAL FIELD-THEORY | LATTICE MODELS | DUALITY | INTEGRABLE STRUCTURE | CHARACTER FORMULA | PHYSICS, PARTICLES & FIELDS | Mathematical analysis | Exteriors | Mathematical models | Spectra | Coupling | Strings | Formalism | Finite difference method | Mathematics | Mathematical Physics | High Energy Physics - Theory | Fysik | Physical Sciences | Naturvetenskap | Natural Sciences

Integrable Field Theories | Supersymmetric gauge theory | AdS-CFT Correspondence | Quantum Physics | Bethe Ansatz | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | Super-symmetric gauge theory | FUNCTIONAL-EQUATIONS | ANALYTIC BETHE-ANSATZ | BAXTERS Q-OPERATORS | CONFORMAL FIELD-THEORY | LATTICE MODELS | DUALITY | INTEGRABLE STRUCTURE | CHARACTER FORMULA | PHYSICS, PARTICLES & FIELDS | Mathematical analysis | Exteriors | Mathematical models | Spectra | Coupling | Strings | Formalism | Finite difference method | Mathematics | Mathematical Physics | High Energy Physics - Theory | Fysik | Physical Sciences | Naturvetenskap | Natural Sciences

Journal Article

Journal of High Energy Physics, ISSN 1029-8479, 2/2019, Volume 2019, Issue 2, pp. 1 - 36

We construct N = 4 D 2 , 1 ; α $$ \mathcal{N}=4D\left(2,1;\ \alpha \right) $$ superconformal quantum mechanical system for any configuration of vectors forming...

Integrable Hierarchies | Extended Supersymmetry | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | WDVV EQUATIONS | CALOGERO | PHYSICS, PARTICLES & FIELDS | Supersymmetry | Mechanical systems | Hamiltonian functions | Quantum mechanics

Integrable Hierarchies | Extended Supersymmetry | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | WDVV EQUATIONS | CALOGERO | PHYSICS, PARTICLES & FIELDS | Supersymmetry | Mechanical systems | Hamiltonian functions | Quantum mechanics

Journal Article

LETTERS IN MATHEMATICAL PHYSICS, ISSN 0377-9017, 05/2020, Volume 110, Issue 5, pp. 969 - 999

We propose quantum Hamiltonians of the double-elliptic many-body integrable system (DELL) and study its spectrum. These Hamiltonians are certain elliptic...

Supersymmetric gauge theories | Elliptic cohomology | Quantum K-theory | DUALITY | Integrable systems | PHYSICS, MATHEMATICAL | Quantum hydrodynamics | Geometric representation theory

Supersymmetric gauge theories | Elliptic cohomology | Quantum K-theory | DUALITY | Integrable systems | PHYSICS, MATHEMATICAL | Quantum hydrodynamics | Geometric representation theory

Journal Article

Physics Letters A, ISSN 0375-9601, 06/2019, Volume 383, Issue 18, pp. 2149 - 2152

We show how to deform separable Hénon-Heiles system with isospectral Lax representation, related with the stationary flow of the 5th-order KdV, to respective...

Frobenius integrable systems | Painlevé equations | Non-autonomous Hamiltonian systems | Isomonodromic Lax representation

Frobenius integrable systems | Painlevé equations | Non-autonomous Hamiltonian systems | Isomonodromic Lax representation

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 02/2018, Volume 364, pp. 27 - 61

We employ the Ablowitz–Ladik system as an illustrative example in order to demonstrate how to analyze initial–boundary value problems for integrable nonlinear...

Integrable system | Initial–boundary value problem | Riemann–Hilbert problem | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PDES | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | Riemann-Hilbert problem | HALF-LINE | Initial-boundary value problem | DIRICHLET | DIFFERENTIAL-DIFFERENCE EQUATIONS | X-3 LAX PAIRS | HIERARCHY | Physics - Exactly Solvable and Integrable Systems

Integrable system | Initial–boundary value problem | Riemann–Hilbert problem | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PDES | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | Riemann-Hilbert problem | HALF-LINE | Initial-boundary value problem | DIRICHLET | DIFFERENTIAL-DIFFERENCE EQUATIONS | X-3 LAX PAIRS | HIERARCHY | Physics - Exactly Solvable and Integrable Systems

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 01/2016, Volume 51, pp. 60 - 67

In the present paper, the prolongation technique and Painlevé analysis are performed to a two-component Korteweg–de Vries system. It is proved that this system...

Fission and fusion behaviors | Painlevé test | Prolongation structure | Auto-Bäcklund transformation | Lax integrable | Painleve test | MATHEMATICS, APPLIED | KDV SYSTEMS | EQUATIONS | PAINLEVE PROPERTY | Auto-Backlund transformation | Algebra

Fission and fusion behaviors | Painlevé test | Prolongation structure | Auto-Bäcklund transformation | Lax integrable | Painleve test | MATHEMATICS, APPLIED | KDV SYSTEMS | EQUATIONS | PAINLEVE PROPERTY | Auto-Backlund transformation | Algebra

Journal Article

Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, 2016, Volume 6, Issue 6, pp. 1 - 51

We review recent progress in understanding the notion of locality in integrable quantum lattice systems. The central concept concerns the so-called quasilocal...

MANY-BODY SYSTEM | ladders and planes | GROUND-STATE | FIELD-THEORIES | THERMODYNAMIC LIMIT | integrable spin chains and vertex models | quantum quenches | quantum transport in one-dimension | PHYSICS, MATHEMATICAL | HUBBARD-MODEL | MECHANICS | DELTA-FUNCTION INTERACTION | QUANTUM-SYSTEMS | CONSERVATION-LAWS | FINITE-TEMPERATURE | spin chains | HEISENBERG-MODEL

MANY-BODY SYSTEM | ladders and planes | GROUND-STATE | FIELD-THEORIES | THERMODYNAMIC LIMIT | integrable spin chains and vertex models | quantum quenches | quantum transport in one-dimension | PHYSICS, MATHEMATICAL | HUBBARD-MODEL | MECHANICS | DELTA-FUNCTION INTERACTION | QUANTUM-SYSTEMS | CONSERVATION-LAWS | FINITE-TEMPERATURE | spin chains | HEISENBERG-MODEL

Journal Article