2004, 1, ISBN 0415298059, xv, 730

Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems...

Geodesic flows | Hamiltonian systems | Geodesics (Mathematics) | Geometry | Differential Equations | Mathematical Analysis

Geodesic flows | Hamiltonian systems | Geodesics (Mathematics) | Geometry | Differential Equations | Mathematical Analysis

Book

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2011, Volume 44, Issue 10, pp. 103001 - 146

T- and Y-systems are ubiquitous structures in classical and quantum integrable systems...

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

Nonlinear dynamics, ISSN 1573-269X, 2017, 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 theory...

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

Proceedings of the National Academy of Sciences - PNAS, ISSN 1091-6490, 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...

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

Letters in mathematical physics, ISSN 1573-0530, 2017, 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 vector fields...

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

Journal of statistical mechanics, ISSN 1742-5468, 2016, Volume 2016, Issue 6, pp. 064008 - 51

We review recent progress in understanding the notion of locality in integrable quantum lattice systems...

Statistical and Nonlinear Physics | Statistics and Probability | Statistics, Probability and Uncertainty | 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

Statistical and Nonlinear Physics | Statistics and Probability | Statistics, Probability and Uncertainty | 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

Communications in mathematical physics, ISSN 1432-0916, 2019, Volume 369, Issue 2, pp. 433 - 456

Weakly nonlinear analysis of resonant PDEs in recent literature has generated a number of resonant systems for slow evolution of the normal mode amplitudes that possess remarkable properties...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | PHYSICS, MATHEMATICAL | Analysis | Resveratrol

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | PHYSICS, MATHEMATICAL | Analysis | Resveratrol

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 4/2018, Volume 2018, Issue 4, pp. 1 - 37

...) $$. The full system admits an SU(2|1) covariant separation into the center-of-mass sector and the quotient...

Superspaces | Extended Supersymmetry | Field Theories in Lower Dimensions | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Matrix Models | Physics | Elementary Particles, Quantum Field Theory | LIE-ALGEBRAS | PARTICLES | MODELS | INTEGRABLE SYSTEMS | FIELD | PHYSICS, PARTICLES & FIELDS | Analysis | Quantum theory | Supersymmetry | Particle spin | Energy spectra | Quantum mechanics

Superspaces | Extended Supersymmetry | Field Theories in Lower Dimensions | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Matrix Models | Physics | Elementary Particles, Quantum Field Theory | LIE-ALGEBRAS | PARTICLES | MODELS | INTEGRABLE SYSTEMS | FIELD | PHYSICS, PARTICLES & FIELDS | Analysis | Quantum theory | Supersymmetry | Particle spin | Energy spectra | Quantum mechanics

Journal Article

The journal of high energy physics, ISSN 1029-8479, 2018, Volume 2018, Issue 2, pp. 1 - 34

We discuss the relation between the cluster integrable systems and q-difference Painlevé equations. The Newton polygons corresponding to these integrable systems are all 16 convex polygons with a single interior point...

Topological Strings | Integrable Hierarchies | Supersymmetric Gauge Theory | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | SYMMETRIES | FIELD-THEORIES | QUANTUM GROUPS | 5-DIMENSIONAL GAUGE-THEORIES | TAU-FUNCTIONS | GEOMETRY | PHYSICS, PARTICLES & FIELDS | Measurement | Permutations | Gauge theory | Deformation | Mathematical analysis | Clusters | Mutation | Polygons | Mathematical Physics | Nuclear and particle physics. Atomic energy. Radioactivity | Nonlinear Sciences | Exactly Solvable and Integrable Systems | High Energy Physics - Theory | Nonlinear Sciences - Exactly Solvable and Integrable Systems

Topological Strings | Integrable Hierarchies | Supersymmetric Gauge Theory | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | SYMMETRIES | FIELD-THEORIES | QUANTUM GROUPS | 5-DIMENSIONAL GAUGE-THEORIES | TAU-FUNCTIONS | GEOMETRY | PHYSICS, PARTICLES & FIELDS | Measurement | Permutations | Gauge theory | Deformation | Mathematical analysis | Clusters | Mutation | Polygons | Mathematical Physics | Nuclear and particle physics. Atomic energy. Radioactivity | Nonlinear Sciences | Exactly Solvable and Integrable Systems | High Energy Physics - Theory | Nonlinear Sciences - Exactly Solvable and Integrable Systems

Journal Article

Scientific reports, ISSN 2045-2322, 2017, Volume 7, Issue 1, pp. 869 - 11

.... Taking KdV and coupled KdV systems as examples, we can find some types of models (AB-KdV systems) to exhibit the existence on the correlated solutions linked with two events...

EQUATIONS | MULTIDISCIPLINARY SCIENCES | Parity

EQUATIONS | MULTIDISCIPLINARY SCIENCES | Parity

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 5/2017, Volume 2017, Issue 5, pp. 1 - 40

.... We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on a chain...

Discrete Symmetries | Random Systems | Lattice Integrable Models | Extended Supersymmetry | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | MODELS | THERMALIZATION | PARASUPERSYMMETRIC QUANTUM-MECHANICS | INDEX | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Supersymmetry | Chains | Correlators | Entangled states | Nuclear and particle physics. Atomic energy. Radioactivity | Condensed Matter - Statistical Mechanics | High Energy Physics - Theory | Condensed Matter - Disordered Systems and Neural Networks

Discrete Symmetries | Random Systems | Lattice Integrable Models | Extended Supersymmetry | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | MODELS | THERMALIZATION | PARASUPERSYMMETRIC QUANTUM-MECHANICS | INDEX | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Supersymmetry | Chains | Correlators | Entangled states | Nuclear and particle physics. Atomic energy. Radioactivity | Condensed Matter - Statistical Mechanics | High Energy Physics - Theory | Condensed Matter - Disordered Systems and Neural Networks

Journal Article

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2017, Volume 50, Issue 46, p. 463001

... integrable nonlinear systems. We first give a brief outline of the historical background of the rogue wave research, including referring to relevant up-to-date experimental results...

modulation instability | rogue wave | integrable turbulence | PHYSICS, MULTIDISCIPLINARY | DAVEY-STEWARTSON EQUATION | BI-HAMILTONIAN STRUCTURES | PETVIASHVILI-I EQUATION | DARK SOLITONS | SCHRODINGER-EQUATION | SELF-FREQUENCY SHIFT | OPTICAL SOLITONS | PHYSICS, MATHEMATICAL | KADOMTSEV-PETVIASHVILI | PEREGRINE SOLITARY WAVES

modulation instability | rogue wave | integrable turbulence | PHYSICS, MULTIDISCIPLINARY | DAVEY-STEWARTSON EQUATION | BI-HAMILTONIAN STRUCTURES | PETVIASHVILI-I EQUATION | DARK SOLITONS | SCHRODINGER-EQUATION | SELF-FREQUENCY SHIFT | OPTICAL SOLITONS | PHYSICS, MATHEMATICAL | KADOMTSEV-PETVIASHVILI | PEREGRINE SOLITARY WAVES

Journal Article

Physics Letters A, ISSN 0375-9601, 12/2016, Volume 380, Issue 47, pp. 3977 - 3982

•Lotka–Volterra systems, skew-symmetric, linear Hamiltonian, Poisson quadratic structures, “strong” Painlevé property...

Strong Painlevé property | Integrable Lotka Volterra systems | EQUATIONS | PHYSICS, MULTIDISCIPLINARY | Strong Painleve property | INTEGRABLE HAMILTONIAN-SYSTEMS

Strong Painlevé property | Integrable Lotka Volterra systems | EQUATIONS | PHYSICS, MULTIDISCIPLINARY | Strong Painleve property | INTEGRABLE HAMILTONIAN-SYSTEMS

Journal Article

Letters in mathematical physics, ISSN 1573-0530, 2017, Volume 108, Issue 3, pp. 499 - 571

.... Starting from classical integrable systems in the sense of Liouville, we explore the notion of non-degenerate singularities and expose recent research in connection with semi-toric systems...

37J35 | Theoretical, Mathematical and Computational Physics | Complex Systems | Quantization | 53D05 | 70H06 | Physics | Classical and quantum integrable systems | Moment (um) maps | Geometry | Spectral theory | Group Theory and Generalizations | 81Q20 | MONODROMY | CONVEXITY | QUANTUM | ALGEBRAIC PROBLEM | PHYSICS, MATHEMATICAL | FOCUS-FOCUS | HAMILTONIAN-SYSTEMS | Moment (um) maps | NORMAL FORMS | MANIFOLDS | SEMIGLOBAL SYMPLECTIC INVARIANTS | Mathematics | Nonlinear Sciences | Symplectic Geometry | Spectral Theory | Exactly Solvable and Integrable Systems

37J35 | Theoretical, Mathematical and Computational Physics | Complex Systems | Quantization | 53D05 | 70H06 | Physics | Classical and quantum integrable systems | Moment (um) maps | Geometry | Spectral theory | Group Theory and Generalizations | 81Q20 | MONODROMY | CONVEXITY | QUANTUM | ALGEBRAIC PROBLEM | PHYSICS, MATHEMATICAL | FOCUS-FOCUS | HAMILTONIAN-SYSTEMS | Moment (um) maps | NORMAL FORMS | MANIFOLDS | SEMIGLOBAL SYMPLECTIC INVARIANTS | Mathematics | Nonlinear Sciences | Symplectic Geometry | Spectral Theory | Exactly Solvable and Integrable Systems

Journal Article