Physics Letters A, ISSN 0375-9601, 02/2018, Volume 382, Issue 5, pp. 253 - 258

... equation.•The discretization of the N=2a=−2 supersymmetric KdV equation is considered.

Supersymmetric integrable system | Nonlinear superposition formula | Bäcklund transformation | Darboux transformation | Discrete integrable system | SOLITON-SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | SUPER-KDV | ALGEBRA | EXTENSION | Backlund transformation | BILINEAR FORM

Supersymmetric integrable system | Nonlinear superposition formula | Bäcklund transformation | Darboux transformation | Discrete integrable system | SOLITON-SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | SUPER-KDV | ALGEBRA | EXTENSION | Backlund transformation | BILINEAR FORM

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 07/2018, Volume 59, Issue 7, p. 72703

.... As an example, we present a few exact discretizations of one-dimensional cubic and quintic Duffing oscillators sharing the form of the Hamiltonian and canonical Poisson...

BACKLUND-TRANSFORMATIONS | MAPS | APPROXIMATION | INTEGRABLE SYSTEMS | DIVISOR | FLOWS | PHYSICS, MATHEMATICAL | EQUATION | EULER TOP

BACKLUND-TRANSFORMATIONS | MAPS | APPROXIMATION | INTEGRABLE SYSTEMS | DIVISOR | FLOWS | PHYSICS, MATHEMATICAL | EQUATION | EULER TOP

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 03/2016, Volume 49, Issue 16, p. 165201

An integrable semi-discrete analogue of the one-dimensional coupled Yajima-Oikawa system, which is comprised of multicomponent short waves and one component...

bright and dark soliton | coupled Yajima-Oikawa system | BKP hierarchy reductions | integrable semi-discretization | NONLINEAR SCHRODINGER-EQUATIONS | INVERSE SCATTERING | PHYSICS, MULTIDISCIPLINARY | FORM | INTERNAL GRAVITY-WAVE | PHYSICS, MATHEMATICAL | ARRAYS | SOLITONS | RESONANT INTERACTION | HIERARCHY | LONG | PACKET

bright and dark soliton | coupled Yajima-Oikawa system | BKP hierarchy reductions | integrable semi-discretization | NONLINEAR SCHRODINGER-EQUATIONS | INVERSE SCATTERING | PHYSICS, MULTIDISCIPLINARY | FORM | INTERNAL GRAVITY-WAVE | PHYSICS, MATHEMATICAL | ARRAYS | SOLITONS | RESONANT INTERACTION | HIERARCHY | LONG | PACKET

Journal Article

Applied and Computational Harmonic Analysis, ISSN 1063-5203, 11/2019, Volume 47, Issue 3, pp. 975 - 1013

We present a novel family of continuous, linear time-frequency transforms adaptable to a multitude of (nonlinear) frequency scales. Similar to classical...

Wavelet | Adapted frequency resolution | Coorbit spaces | Time-frequency | Continuous frames | Banach frames | Warping | Gabor | Atomic decompositions | MATHEMATICS, APPLIED | INTEGRABLE GROUP-REPRESENTATIONS | GABOR FRAMES

Wavelet | Adapted frequency resolution | Coorbit spaces | Time-frequency | Continuous frames | Banach frames | Warping | Gabor | Atomic decompositions | MATHEMATICS, APPLIED | INTEGRABLE GROUP-REPRESENTATIONS | GABOR FRAMES

Journal Article

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 12/2015, Volume 471, Issue 2184, p. 20150390

.... Here we generalize Kahan's method to cubic resp. higher degree polynomial vector fields and show that the resulting discretization also preserves modified versions of the measure and energy when applied to cubic resp...

Kahan's Method | Polarization | Geometric Integration | INTEGRABILITY | Kahan's method | MULTIDISCIPLINARY SCIENCES | DYNAMICS | HIROTA-KIMURA TYPE | SYSTEMS | polarization | geometric integration

Kahan's Method | Polarization | Geometric Integration | INTEGRABILITY | Kahan's method | MULTIDISCIPLINARY SCIENCES | DYNAMICS | HIROTA-KIMURA TYPE | SYSTEMS | polarization | geometric integration

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 05/2016, Volume 49, Issue 22, p. 225201

We prove the Liouville and superintegrability of a generalized Lotka-Volterra system and its Kahan discretization.

superintegrability | Kahan discretization | integrable systems | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

superintegrability | Kahan discretization | integrable systems | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

Journal Article

Regular and Chaotic Dynamics, ISSN 1560-3547, 11/2018, Volume 23, Issue 6, pp. 785 - 796

.... As an example, we present a few new discretizations of motion of the Euler top sharing the integrals of motion with the continuous time system and the Poisson bracket...

37J35 | Euler top | arithmetic of divisors | 70H06 | Mathematics | Dynamical Systems and Ergodic Theory | finite-difference equations | MATHEMATICS, APPLIED | MECHANICS | BACKLUND-TRANSFORMATIONS | INTEGRABLE SYSTEMS | SEPARATION | PHYSICS, MATHEMATICAL

37J35 | Euler top | arithmetic of divisors | 70H06 | Mathematics | Dynamical Systems and Ergodic Theory | finite-difference equations | MATHEMATICS, APPLIED | MECHANICS | BACKLUND-TRANSFORMATIONS | INTEGRABLE SYSTEMS | SEPARATION | PHYSICS, MATHEMATICAL

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 07/2017, Volume 117, pp. 36 - 49

... functions is introduced. Using the discretization techniques for 2D-continuous wavelet transform of the SIM(2...

Wavelets | square-integrable representation | Discretization | Quaternion | Affine group | MATHEMATICS | PHYSICS, MATHEMATICAL | Computer science

Wavelets | square-integrable representation | Discretization | Quaternion | Affine group | MATHEMATICS | PHYSICS, MATHEMATICAL | Computer science

Journal Article

9.
Full Text
Integrable semi-discretization of the massive Thirring system in laboratory coordinates

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 2019, Volume 52, Issue 3, p. 3

Several integrable semi-discretizations are known in the literature for the massive Thirring system in characteristic coordinates...

laboratory and characteristic coordinates | Ablowitz Ladik lattice | massive Thirring model | Bäcklund transformation | integrable semi-discretization | S-MATRIX | REGULARITY WELL-POSEDNESS | Ablowitz-Ladik lattice | PHYSICS, MULTIDISCIPLINARY | MODEL | PHYSICS, MATHEMATICAL | ORBITAL STABILITY | SOLITONS | NONLINEAR DIRAC EQUATIONS | Backlund transformation

laboratory and characteristic coordinates | Ablowitz Ladik lattice | massive Thirring model | Bäcklund transformation | integrable semi-discretization | S-MATRIX | REGULARITY WELL-POSEDNESS | Ablowitz-Ladik lattice | PHYSICS, MULTIDISCIPLINARY | MODEL | PHYSICS, MATHEMATICAL | ORBITAL STABILITY | SOLITONS | NONLINEAR DIRAC EQUATIONS | Backlund transformation

Journal Article

Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, 01/2018, Volume 25, Issue 1, pp. 166 - 177

We consider the discretization of Darboux integrable equations. For each of the integrals of a Laine equation we constructed either a semi-discrete equation...

Darboux integrability | n-integral | Semi-discrete chain | x-integral | discretization | MATHEMATICS, APPLIED | MODELS | CLASSIFICATION | LIOUVILLE TYPE | PHYSICS, MATHEMATICAL

Darboux integrability | n-integral | Semi-discrete chain | x-integral | discretization | MATHEMATICS, APPLIED | MODELS | CLASSIFICATION | LIOUVILLE TYPE | PHYSICS, MATHEMATICAL

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 04/2015, Volume 56, Issue 4, p. 43502

In the present paper, we mainly study the integrable semi-discretization of a multicomponent short pulse equation...

PHYSICS, MATHEMATICAL | ULTRA-SHORT PULSES | PROPAGATION | NONLINEAR MEDIA | Transformations (mathematics) | Discretization | Mathematical analysis | Physics - Exactly Solvable and Integrable Systems

PHYSICS, MATHEMATICAL | ULTRA-SHORT PULSES | PROPAGATION | NONLINEAR MEDIA | Transformations (mathematics) | Discretization | Mathematical analysis | Physics - Exactly Solvable and Integrable Systems

Journal Article

International Journal of Theoretical Physics, ISSN 0020-7748, 7/2018, Volume 57, Issue 7, pp. 2093 - 2102

We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature...

Yang-Mills theory | Theoretical, Mathematical and Computational Physics | Gauge invariance | Quantum Physics | Physics, general | Physics | Elementary Particles, Quantum Field Theory | Discretized model | Business administration | Pattern Formation and Solitons | Mathematical Physics | Analysis of PDEs | Library and information sciences | Operator Algebras | Mathematics | Nonlinear Sciences | Humanities and Social Sciences | General Mathematics | Chaotic Dynamics | Spectral Theory | Differential Geometry | Metric Geometry | Exactly Solvable and Integrable Systems

Yang-Mills theory | Theoretical, Mathematical and Computational Physics | Gauge invariance | Quantum Physics | Physics, general | Physics | Elementary Particles, Quantum Field Theory | Discretized model | Business administration | Pattern Formation and Solitons | Mathematical Physics | Analysis of PDEs | Library and information sciences | Operator Algebras | Mathematics | Nonlinear Sciences | Humanities and Social Sciences | General Mathematics | Chaotic Dynamics | Spectral Theory | Differential Geometry | Metric Geometry | Exactly Solvable and Integrable Systems

Journal Article

13.
Full Text
On the multi-symplectic structure of Boussinesq-type systems. II: Geometric discretization

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 10/2019, Volume 397, pp. 1 - 16

.... By using the method of lines, the geometric properties, based on the multi-symplectic and Hamiltonian structures, of different strategies for the spatial and time discretizations are discussed and illustrated...

Symplectic methods | Multi-symplectic schemes | Boussinesq equations | Surface waves | Geometric numerical integration | DERIVATION | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PDES | EQUATIONS | BACKWARD ERROR ANALYSIS | PHYSICS, MATHEMATICAL | AMPLITUDE LONG WAVES | NONLINEAR DISPERSIVE MEDIA | NUMERICAL SCHEMES | INTEGRATORS | Analysis | Wave propagation | Fluid Dynamics | Computational Physics | Pattern Formation and Solitons | Atmospheric and Oceanic Physics | Analysis of PDEs | Numerical Analysis | Mechanics | Mechanics of the fluids | Mathematics | Nonlinear Sciences | Exactly Solvable and Integrable Systems | Physics

Symplectic methods | Multi-symplectic schemes | Boussinesq equations | Surface waves | Geometric numerical integration | DERIVATION | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PDES | EQUATIONS | BACKWARD ERROR ANALYSIS | PHYSICS, MATHEMATICAL | AMPLITUDE LONG WAVES | NONLINEAR DISPERSIVE MEDIA | NUMERICAL SCHEMES | INTEGRATORS | Analysis | Wave propagation | Fluid Dynamics | Computational Physics | Pattern Formation and Solitons | Atmospheric and Oceanic Physics | Analysis of PDEs | Numerical Analysis | Mechanics | Mechanics of the fluids | Mathematics | Nonlinear Sciences | Exactly Solvable and Integrable Systems | Physics

Journal Article

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, ISSN 1364-5021, 03/2019, Volume 475, Issue 2223, p. 20180761

Kahan discretization is applicable to any quadratic vector field and produces a birational map which approximates the shift along the phase flow...

elliptic curve | INTEGRABILITY | integrable maps | MULTIDISCIPLINARY SCIENCES | integrable discretization | Hamiltonian vector field | Manin transformation | 1008 | Manintransformation | 120

elliptic curve | INTEGRABILITY | integrable maps | MULTIDISCIPLINARY SCIENCES | integrable discretization | Hamiltonian vector field | Manin transformation | 1008 | Manintransformation | 120

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 02/2010, Volume 43, Issue 8, pp. 085203 - 085203

...Home Search Collections Journals About Contact us My IOPscience Integrable discretizations of the short pulse equation This article has been downloaded...

PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | SINE-GORDON EQUATION | NONLINEAR MEDIA | Construction | Numerical analysis | Discretization | Mathematical analysis | Determinants | Mathematical models | Short pulses

PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | SINE-GORDON EQUATION | NONLINEAR MEDIA | Construction | Numerical analysis | Discretization | Mathematical analysis | Determinants | Mathematical models | Short pulses

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 03/2019, Volume 60, Issue 3, p. 33502

...Journal of Mathematical Physics ARTICLE scitation.org/journal/jmp Time discretization of the spin Calogero-Moser model and the semi-discrete matrix KP...

SYSTEMS | PHYSICS, MATHEMATICAL | KADOMTSEV-PETVIASHVILI EQUATION | ELLIPTIC SOLUTIONS | Poles | Equations of motion

SYSTEMS | PHYSICS, MATHEMATICAL | KADOMTSEV-PETVIASHVILI EQUATION | ELLIPTIC SOLUTIONS | Poles | Equations of motion

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 11/2009, Volume 42, Issue 46, pp. 465203 - 465203 (8)

...Home Search Collections Journals About Contact us My IOPscience The Kundu–Eckhaus equation and its discretizations This article has been downloaded...

PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 12/2015, Volume 49, Issue 3, p. 35201

.... The ODEs are continuous limits of the O Delta Ss, or conversely, the O Delta Ss are invariant discretizations of the ODEs...

Lie symmetries | numerical analysis | difference equations | MOVING COFRAMES | PHYSICS, MULTIDISCIPLINARY | POINT SYMMETRIES | ALGEBRA | PHYSICS, MATHEMATICAL | SCHEMES | Discretization | Dependent variables | Mathematical analysis | Differential equations | Mathematical models | Invariants | Standards | Symmetry

Lie symmetries | numerical analysis | difference equations | MOVING COFRAMES | PHYSICS, MULTIDISCIPLINARY | POINT SYMMETRIES | ALGEBRA | PHYSICS, MATHEMATICAL | SCHEMES | Discretization | Dependent variables | Mathematical analysis | Differential equations | Mathematical models | Invariants | Standards | Symmetry

Journal Article

Regular and Chaotic Dynamics, ISSN 1560-3547, 7/2017, Volume 22, Issue 4, pp. 353 - 367

.... We discuss integrable discretizations and deformations of this nonholonomic system using the same Abel quadratures...

37J35 | Abel quadratures | 70H33 | nonholonomic systems | arithmetic of divisors | 37J60 | Mathematics | Dynamical Systems and Ergodic Theory | 37K20 | MATHEMATICS, APPLIED | MECHANICS | EXPLICIT INTEGRATION | BACKLUND-TRANSFORMATIONS | PLANE | DYNAMICS | SYSTEMS | PHYSICS, MATHEMATICAL | HIERARCHY | Numerical integration | Research | Mathematical research | Geometry, Differential

37J35 | Abel quadratures | 70H33 | nonholonomic systems | arithmetic of divisors | 37J60 | Mathematics | Dynamical Systems and Ergodic Theory | 37K20 | MATHEMATICS, APPLIED | MECHANICS | EXPLICIT INTEGRATION | BACKLUND-TRANSFORMATIONS | PLANE | DYNAMICS | SYSTEMS | PHYSICS, MATHEMATICAL | HIERARCHY | Numerical integration | Research | Mathematical research | Geometry, Differential

Journal Article

Journal of the Physical Society of Japan, ISSN 0031-9015, 2008, Volume 77, Issue 7, pp. 074001 - 074001

The maximal super-integrability of a discretization of the Calogero-Moser model introduced by Nijhoff and Pang is presented...

super-integrability | Calogero-Moser model | integrable discretization | Super-integrability | Integrable discretization | BODY PROBLEMS | PHYSICS, MULTIDISCIPLINARY | SYSTEMS | KEPLER MOTION | SUPERINTEGRABILITY | Physics - Exactly Solvable and Integrable Systems

super-integrability | Calogero-Moser model | integrable discretization | Super-integrability | Integrable discretization | BODY PROBLEMS | PHYSICS, MULTIDISCIPLINARY | SYSTEMS | KEPLER MOTION | SUPERINTEGRABILITY | Physics - Exactly Solvable and Integrable Systems

Journal Article

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