2016, Second edition., Graduate studies in mathematics, ISBN 1470409860, Volume 175., xviii, 453 pages

Book

Optics Letters, ISSN 0146-9592, 04/2017, Volume 42, Issue 7, pp. 1197 - 1200

Leveraging subwavelength resonant nanostructures, plasmonic metasurfaces have recently attracted much attention as a breakthrough concept for engineering...

OPTICS | Mathematical analysis | Magnetic resonance | Differential equations | Constants | Mathematical models | Nanostructure | Dielectrics | Invariants

OPTICS | Mathematical analysis | Magnetic resonance | Differential equations | Constants | Mathematical models | Nanostructure | Dielectrics | Invariants

Journal Article

Bernoulli, ISSN 1350-7265, 02/2017, Volume 23, Issue 1, pp. 645 - 669

This paper focuses on stochastic partial differential equations (SPDEs) under two-time-scale formulation. Distinct from the work in the existing literature,...

Strong convergence | Stochastic partial differential equation | Averaging principle | Invariant measure | α-stable process | invariant measure | STATISTICS & PROBABILITY | alpha-stable process | stochastic partial differential equation | strong convergence | averaging principle

Strong convergence | Stochastic partial differential equation | Averaging principle | Invariant measure | α-stable process | invariant measure | STATISTICS & PROBABILITY | alpha-stable process | stochastic partial differential equation | strong convergence | averaging principle

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2016, Volume 440, Issue 1, pp. 286 - 299

The method of linear determining equations is developed to study conditional Lie–Bäcklund symmetries for evolution equations, which is more general than the...

Symmetry reduction | Linear determining equation | Conditional Lie–Bäcklund symmetry | Inhomogeneous nonlinear diffusion equation | Differential constraint | Conditional Lie-Bäcklund symmetry | Conditional Lie-Backlund symmetry | MATHEMATICS, APPLIED | NONINTEGRABLE EQUATIONS | CLASSIFICATION | EVOLUTION-EQUATIONS | MATHEMATICS | POTENTIAL SYMMETRIES | WAVES | INVARIANT SUBSPACES | REDUCTION | VARIABLES | SEPARATION

Symmetry reduction | Linear determining equation | Conditional Lie–Bäcklund symmetry | Inhomogeneous nonlinear diffusion equation | Differential constraint | Conditional Lie-Bäcklund symmetry | Conditional Lie-Backlund symmetry | MATHEMATICS, APPLIED | NONINTEGRABLE EQUATIONS | CLASSIFICATION | EVOLUTION-EQUATIONS | MATHEMATICS | POTENTIAL SYMMETRIES | WAVES | INVARIANT SUBSPACES | REDUCTION | VARIABLES | SEPARATION

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 02/2016, Volume 260, Issue 3, pp. 2354 - 2382

In this paper, we explain in more details the modern treatment of the problem of group classification of (systems of) partial differential equations (PDEs)...

Symmetry reduction | Group classification | Invariant solutions | Equivalence transformation | Generalized Zakharov–Kuznetsov equations | Generalized Zakharov-Kuznetsov equations | TANH | SYMMETRIES | STABILITY | SOLITARY | SHALLOW-WATER EQUATIONS | MATHEMATICS | WAVES | SOLITONS | Algebra | Algorithms | Differential equations

Symmetry reduction | Group classification | Invariant solutions | Equivalence transformation | Generalized Zakharov–Kuznetsov equations | Generalized Zakharov-Kuznetsov equations | TANH | SYMMETRIES | STABILITY | SOLITARY | SHALLOW-WATER EQUATIONS | MATHEMATICS | WAVES | SOLITONS | Algebra | Algorithms | Differential equations

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 2015, Volume 80, Issue 1-2, pp. 447 - 455

A systematic method is given to derive Lie point symmetries of nonlinear fractional ordinary differential equations and illustrate its applicability through...

Fractional ordinary differential equations | Riemann–Liouville fractional derivative | Mittag-Leffler function | Lie symmetry analysis | MECHANICS | Riemann-Liouville fractional derivative | TRANSFORMATIONS | ENGINEERING, MECHANICAL | Analysis | Differential equations | Ordinary differential equations | Nonlinear equations | Riccati equation | Mathematical analysis | Nonlinear analysis | Exact solutions | Nonlinearity | Derivatives | Dynamical systems | Invariants | Symmetry

Fractional ordinary differential equations | Riemann–Liouville fractional derivative | Mittag-Leffler function | Lie symmetry analysis | MECHANICS | Riemann-Liouville fractional derivative | TRANSFORMATIONS | ENGINEERING, MECHANICAL | Analysis | Differential equations | Ordinary differential equations | Nonlinear equations | Riccati equation | Mathematical analysis | Nonlinear analysis | Exact solutions | Nonlinearity | Derivatives | Dynamical systems | Invariants | Symmetry

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 11/2018, Volume 41, Issue 16, pp. 6955 - 6967

The linearization problem for scalar third‐order ordinary differential equations via point transformations was solved partially in the works of Al‐Dweik et al...

point transformations | Cartan's equivalence method | scalar third‐order ordinary differential equation | linearization problem | scalar third-order ordinary differential equation | MATHEMATICS, APPLIED | SYMMETRY GROUP | CLASSIFICATION | Transformations (mathematics) | Equivalence | Mathematical analysis | Differential equations | Lie groups | Ordinary differential equations | Invariants | Linearization

point transformations | Cartan's equivalence method | scalar third‐order ordinary differential equation | linearization problem | scalar third-order ordinary differential equation | MATHEMATICS, APPLIED | SYMMETRY GROUP | CLASSIFICATION | Transformations (mathematics) | Equivalence | Mathematical analysis | Differential equations | Lie groups | Ordinary differential equations | Invariants | Linearization

Journal Article

2011, World Scientific series on nonlinear science. Series A, Monographs and treatises, ISBN 9789814329064, Volume 78, ix, 312

Book

Journal of High Energy Physics, ISSN 1126-6708, 8/2018, Volume 2018, Issue 8, pp. 1 - 72

Every four-dimensional N=2 $$ \mathcal{N}=2 $$ superconformal field theory comes equipped with an intricate algebraic invariant, the associated vertex operator...

Conformal Field Theory | Extended Supersymmetry | 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 | FORMS | QUIVER VARIETIES | CLASSIFICATION | PHYSICS, PARTICLES & FIELDS | Algebra | Differential equations | Mathematical analysis | Lie groups | Field theory | Vectors (mathematics) | Invariants | Physics - High Energy Physics - Theory | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory

Conformal Field Theory | Extended Supersymmetry | 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 | FORMS | QUIVER VARIETIES | CLASSIFICATION | PHYSICS, PARTICLES & FIELDS | Algebra | Differential equations | Mathematical analysis | Lie groups | Field theory | Vectors (mathematics) | Invariants | Physics - High Energy Physics - Theory | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 04/2012, Volume 241, Issue 7, pp. 764 - 774

A new family of solutions of the Jacobi partial differential equations for finite-dimensional Poisson systems is investigated. This family is mathematically...

Poisson structures | Casimir invariants | Jacobi partial differential equations | Finite-dimensional Poisson systems | MATHEMATICS, APPLIED | IDENTITIES | PHYSICS, MULTIDISCIPLINARY | PHYSICS, FLUIDS & PLASMAS | BI-HAMILTONIAN STRUCTURE | FORMULATION | PHYSICS, MATHEMATICAL | FAMILY | DYNAMICAL-SYSTEMS | LOTKA-VOLTERRA EQUATIONS | SEPARATION | TODA | Differential equations | Construction | Infinity | Partial differential equations | Mathematical analysis | Focusing | Canonical forms | Nonlinearity | Invariants

Poisson structures | Casimir invariants | Jacobi partial differential equations | Finite-dimensional Poisson systems | MATHEMATICS, APPLIED | IDENTITIES | PHYSICS, MULTIDISCIPLINARY | PHYSICS, FLUIDS & PLASMAS | BI-HAMILTONIAN STRUCTURE | FORMULATION | PHYSICS, MATHEMATICAL | FAMILY | DYNAMICAL-SYSTEMS | LOTKA-VOLTERRA EQUATIONS | SEPARATION | TODA | Differential equations | Construction | Infinity | Partial differential equations | Mathematical analysis | Focusing | Canonical forms | Nonlinearity | Invariants

Journal Article

1972, Mathematics in science and engineering, ISBN 0120579502, Volume 88, xi, 204

Book

Applied Mathematical Modelling, ISSN 0307-904X, 12/2016, Volume 40, Issue 23-24, pp. 10286 - 10299

•Numerical solution of delay and partial delay differential equations are considered.•Haar wavelet collocation method is applied.•The method works equally good...

Time-varying delay system | Delay partial differential equations | Time-invariant delay system | Delay differential equations | Haar wavelet | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | PARAMETER-ESTIMATION | BLOCK-PULSE FUNCTIONS | SYSTEMS | TIME | Differential equations

Time-varying delay system | Delay partial differential equations | Time-invariant delay system | Delay differential equations | Haar wavelet | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | PARAMETER-ESTIMATION | BLOCK-PULSE FUNCTIONS | SYSTEMS | TIME | Differential equations

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 10/2017, Volume 263, Issue 8, pp. 4929 - 4977

In this paper, we study the Wong–Zakai approximations given by a stationary process via the Wiener shift and their associated dynamics of the stochastic...

Brownian motion | Wong–Zakai approximations | Multiplicative noise | Random dynamical systems | Center manifolds | BROWNIAN-MOTION | THEOREM | CHAOTIC BEHAVIOR | DRIVEN | INVARIANT-MANIFOLDS | UNSTABLE MANIFOLDS | INTEGRALS | MATHEMATICS | Wong-Zalmi approximations | BANACH-SPACES | CONVERGENCE | POINT | Differential equations

Brownian motion | Wong–Zakai approximations | Multiplicative noise | Random dynamical systems | Center manifolds | BROWNIAN-MOTION | THEOREM | CHAOTIC BEHAVIOR | DRIVEN | INVARIANT-MANIFOLDS | UNSTABLE MANIFOLDS | INTEGRALS | MATHEMATICS | Wong-Zalmi approximations | BANACH-SPACES | CONVERGENCE | POINT | Differential equations

Journal Article

Theoretical and Mathematical Physics(Russian Federation), ISSN 0040-5779, 2015, Volume 182, Issue 2, pp. 211 - 230

All Painleve equations except the first belong to one type of equations. In terms of invariants of these equations, we obtain criteria for the equivalence to...

equivalence | Painlevé equation | invariant | Differential equations

equivalence | Painlevé equation | invariant | Differential equations

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 7/2016, Volume 85, Issue 1, pp. 659 - 673

Given a time fractional nonlinear partial differential equation, we show how to derive its exact solution using invariant subspace method. This has been...

Invariant subspace method | Engineering | Vibration, Dynamical Systems, Control | Time fractional nonlinear PDEs | Mechanics | Automotive Engineering | Laplace transform method | Mechanical Engineering | Mittag–Leffler function | Caputo fractional derivative | MECHANICS | Mittag-Leffler function | DECOMPOSITION | ENGINEERING, MECHANICAL | Thin films | Differential equations | Dielectric films | Quadratic equations | Nonlinear equations | Boussinesq equations | Partial differential equations | Nonlinear differential equations | Exact solutions | Wave equations | Subspace methods | Convection | Invariants | Mathematical analysis | Subspaces

Invariant subspace method | Engineering | Vibration, Dynamical Systems, Control | Time fractional nonlinear PDEs | Mechanics | Automotive Engineering | Laplace transform method | Mechanical Engineering | Mittag–Leffler function | Caputo fractional derivative | MECHANICS | Mittag-Leffler function | DECOMPOSITION | ENGINEERING, MECHANICAL | Thin films | Differential equations | Dielectric films | Quadratic equations | Nonlinear equations | Boussinesq equations | Partial differential equations | Nonlinear differential equations | Exact solutions | Wave equations | Subspace methods | Convection | Invariants | Mathematical analysis | Subspaces

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 02/2017, Volume 262, Issue 3, pp. 1603 - 1616

Asymptotic stability is examined for singularly perturbed ordinary differential equations that may not possess a natural split into fast and slow motions....

Asymptotic stability | Singular perturbations | Young measures | Invariant measures | MATHEMATICS | Differential equations

Asymptotic stability | Singular perturbations | Young measures | Invariant measures | MATHEMATICS | Differential equations

Journal Article

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2017, Volume 55, Issue 2, pp. 1153 - 1178

This paper investigates the asymptotic behavior of solutions to certain in finite systems of ordinary differential equations. In particular, we use results...

Ergodic theory | C0-semigroup | Rates of convergence | Asymptotic behavior | Ordinary differential equations | System | Spectrum | LAPLACE TRANSFORMS | MATHEMATICS, APPLIED | DECAY | STRING STABILITY | ergodic theory | rates of convergence | ordinary differential equations | SEMIGROUPS | C-0-semigroup | system | asymptotic behavior | TAUBERIAN-THEOREMS | spectrum | SPATIALLY INVARIANT-SYSTEMS | AUTOMATION & CONTROL SYSTEMS

Ergodic theory | C0-semigroup | Rates of convergence | Asymptotic behavior | Ordinary differential equations | System | Spectrum | LAPLACE TRANSFORMS | MATHEMATICS, APPLIED | DECAY | STRING STABILITY | ergodic theory | rates of convergence | ordinary differential equations | SEMIGROUPS | C-0-semigroup | system | asymptotic behavior | TAUBERIAN-THEOREMS | spectrum | SPATIALLY INVARIANT-SYSTEMS | AUTOMATION & CONTROL SYSTEMS

Journal Article

Modern Physics Letters B, ISSN 0217-9849, 01/2020, Volume 34, Issue 1, p. 2050009

The invariant subspace method (ISM) is a powerful tool for investigating analytical solutions to fractional differential–difference equations (FDDEs). Based on...

Invariant subspace method | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | fractional differential-difference equations | Caputo derivative | PHYSICS, MATHEMATICAL | analytical solutions

Invariant subspace method | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | fractional differential-difference equations | Caputo derivative | PHYSICS, MATHEMATICAL | analytical solutions

Journal Article

Journal of Symbolic Computation, ISSN 0747-7171, 05/2018, Volume 86, pp. 166 - 188

Algorithms for embedding certain types of nilpotent subalgebras in maximal subalgebras of the same type are developed, using methods of real algebraic groups....

Maximal solvable subalgebras | Invariant solutions | Algebraic Lie algebras | LIE-ALGEBRAS | FORMS | DECOMPOSITIONS | MATHEMATICS, APPLIED | SYMMETRIES | COMPUTER SCIENCE, THEORY & METHODS | SUBGROUPS | Electrical engineering | Computer science | Algorithms | Algebra | Differential equations

Maximal solvable subalgebras | Invariant solutions | Algebraic Lie algebras | LIE-ALGEBRAS | FORMS | DECOMPOSITIONS | MATHEMATICS, APPLIED | SYMMETRIES | COMPUTER SCIENCE, THEORY & METHODS | SUBGROUPS | Electrical engineering | Computer science | Algorithms | Algebra | Differential equations

Journal Article

20.
Full Text
Ergodicity of scalar stochastic differential equations with Hölder continuous coefficients

Stochastic Processes and their Applications, ISSN 0304-4149, 10/2018, Volume 128, Issue 10, pp. 3253 - 3272

It is well-known that for a one dimensional stochastic differential equation driven by Brownian noise, with coefficient functions satisfying the assumptions of...

Cox–Ingersoll–Ross model | Wright–Fisher model | Kullback–Leibler divergence | Fokker–Planck equation | Invariant measure | Stationary distributions | Ait-Sahalia model | MODELS | Cox-Ingersoll-Ross model | MEASURE ATTRACTORS | STATISTICS & PROBABILITY | Kullback-Leibler divergence | Wright-Fisher model | Fokker-Planck equation | Population genetics | Analysis | Differential equations

Cox–Ingersoll–Ross model | Wright–Fisher model | Kullback–Leibler divergence | Fokker–Planck equation | Invariant measure | Stationary distributions | Ait-Sahalia model | MODELS | Cox-Ingersoll-Ross model | MEASURE ATTRACTORS | STATISTICS & PROBABILITY | Kullback-Leibler divergence | Wright-Fisher model | Fokker-Planck equation | Population genetics | Analysis | Differential equations

Journal Article

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