1.
Classical methods in ordinary differential equations

: with applications to boundary value problems

2012, Graduate studies in mathematics, ISBN 0821846949, Volume 129, xvii, 373

Book

1990, Mathematics and its applications (Soviet series), ISBN 9780792305859, Volume 55, x, 220

Book

Geophysical Journal International, ISSN 0956-540X, 2016, Volume 204, Issue 2, pp. 1216 - 1221

This paper presents a generalized wave equation which unifies viscoelastic and pure elastic cases into a single wave equation. In the generalized wave...

Seismic attenuation | Non-linear differential equation | Wave propagation | DISSIPATION | FREQUENCY-RANGE | LINEAR MODELS | GEOCHEMISTRY & GEOPHYSICS | MARINE-SEDIMENTS | ELASTIC WAVES | POWER-LAW ATTENUATION | LOSSY MEDIA | SOUND | PROPAGATION

Seismic attenuation | Non-linear differential equation | Wave propagation | DISSIPATION | FREQUENCY-RANGE | LINEAR MODELS | GEOCHEMISTRY & GEOPHYSICS | MARINE-SEDIMENTS | ELASTIC WAVES | POWER-LAW ATTENUATION | LOSSY MEDIA | SOUND | PROPAGATION

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 10/2013, Volume 222, pp. 255 - 264

In this paper, we propose a new Jacobiâ€“Gaussâ€“Lobatto collocation method for solving the generalized Fitzhughâ€“Nagumo equation. The Jacobiâ€“Gaussâ€“Lobatto points...

Generalized Fitzhughâ€“Nagumo equation | Real Newellâ€“Whitehead equation | Time-dependent Fitzhughâ€“Nagumo equation | Collocation method | Implicit Rungeâ€“Kutta method | Jacobiâ€“Gaussâ€“Lobatto quadrature | Implicit Runge-Kutta method | Generalized Fitzhugh-Nagumo equation | Jacobi-Gauss-Lobatto quadrature | Real Newell-Whitehead equation | Time-dependent Fitzhugh-Nagumo equation | APPROXIMATE SOLUTIONS | MATHEMATICS, APPLIED | HEAT-TRANSFER | DIFFERENTIAL-EQUATIONS | REACTION-DIFFUSION EQUATION | HOMOTOPY ANALYSIS METHOD | SOLITON-SOLUTIONS | NUMERICAL-SOLUTIONS | NON-LINEAR DIFFUSION | BURGERS-EQUATION | NONLINEAR EVOLUTION-EQUATIONS | Methods | Algorithms

Generalized Fitzhughâ€“Nagumo equation | Real Newellâ€“Whitehead equation | Time-dependent Fitzhughâ€“Nagumo equation | Collocation method | Implicit Rungeâ€“Kutta method | Jacobiâ€“Gaussâ€“Lobatto quadrature | Implicit Runge-Kutta method | Generalized Fitzhugh-Nagumo equation | Jacobi-Gauss-Lobatto quadrature | Real Newell-Whitehead equation | Time-dependent Fitzhugh-Nagumo equation | APPROXIMATE SOLUTIONS | MATHEMATICS, APPLIED | HEAT-TRANSFER | DIFFERENTIAL-EQUATIONS | REACTION-DIFFUSION EQUATION | HOMOTOPY ANALYSIS METHOD | SOLITON-SOLUTIONS | NUMERICAL-SOLUTIONS | NON-LINEAR DIFFUSION | BURGERS-EQUATION | NONLINEAR EVOLUTION-EQUATIONS | Methods | Algorithms

Journal Article

Inverse Problems, ISSN 0266-5611, 12/2006, Volume 22, Issue 6, pp. 2197 - 2207

An inverse scattering method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless...

BREAKING | MATHEMATICS, APPLIED | WAVES | INTEGRABILITY | CONSERVED QUANTITIES | SOLITON-SOLUTIONS | STABILITY | GEODESIC-FLOW | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATION | PEAKONS | HIERARCHY | Physics - Exactly Solvable and Integrable Systems

BREAKING | MATHEMATICS, APPLIED | WAVES | INTEGRABILITY | CONSERVED QUANTITIES | SOLITON-SOLUTIONS | STABILITY | GEODESIC-FLOW | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATION | PEAKONS | HIERARCHY | Physics - Exactly Solvable and Integrable Systems

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2011, Volume 74, Issue 18, pp. 7543 - 7561

In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on a Banach space with locally monotone operators, which...

Porous medium equation | [formula omitted]-Laplace equation | Pseudo-monotone | Reactionâ€“diffusion equation | Navierâ€“Stokes equation | Locally monotone | Nonlinear evolution equation | Burgers equation | Reactiondiffusion equation | p-Laplace equation | NavierStokes equation | MATHEMATICS, APPLIED | FAST-DIFFUSION-EQUATIONS | SPACES | ATTRACTOR | MODEL | Navier-Stokes equation | MATHEMATICS | Reaction-diffusion equation | GENERALIZED POROUS-MEDIA | HARNACK INEQUALITY | NON-LINEAR EQUATIONS | Operators | Mathematical analysis | Uniqueness | Nonlinear evolution equations | Mathematical models | Three dimensional | Navier-Stokes equations

Porous medium equation | [formula omitted]-Laplace equation | Pseudo-monotone | Reactionâ€“diffusion equation | Navierâ€“Stokes equation | Locally monotone | Nonlinear evolution equation | Burgers equation | Reactiondiffusion equation | p-Laplace equation | NavierStokes equation | MATHEMATICS, APPLIED | FAST-DIFFUSION-EQUATIONS | SPACES | ATTRACTOR | MODEL | Navier-Stokes equation | MATHEMATICS | Reaction-diffusion equation | GENERALIZED POROUS-MEDIA | HARNACK INEQUALITY | NON-LINEAR EQUATIONS | Operators | Mathematical analysis | Uniqueness | Nonlinear evolution equations | Mathematical models | Three dimensional | Navier-Stokes equations

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 09/2018, Volume 378-379, pp. 1 - 19

In this paper, we study entire solutions of the Allenâ€“Cahn equation in one-dimensional Euclidean space. This equation is a scalar reactionâ€“diffusion equation...

Entire solution | Superâ€“sub-solutions | Reactionâ€“diffusion equation | Traveling front | REACTION-DIFFUSION EQUATIONS | MATHEMATICS, APPLIED | TRAVELING FRONTS | PHYSICS, MULTIDISCIPLINARY | Super-sub-solutions | PHYSICS, MATHEMATICAL | Reaction-diffusion equation | KPP EQUATION | NON-LINEAR DIFFUSION | SYSTEMS | Traveling | LATTICE

Entire solution | Superâ€“sub-solutions | Reactionâ€“diffusion equation | Traveling front | REACTION-DIFFUSION EQUATIONS | MATHEMATICS, APPLIED | TRAVELING FRONTS | PHYSICS, MULTIDISCIPLINARY | Super-sub-solutions | PHYSICS, MATHEMATICAL | Reaction-diffusion equation | KPP EQUATION | NON-LINEAR DIFFUSION | SYSTEMS | Traveling | LATTICE

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 05/2009, Volume 14, Issue 5, pp. 2034 - 2045

Non-linear SchrÃ¶dinger equation for optical medias with saturable non-linear refractive index is obtained and numerical calculation method is applied and...

Solitary solutions | Non-linear SchrÃ¶dinger equation | Non-linear effects | Saturable soliton | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | COLLISION | PHYSICS, MATHEMATICAL | Non-linear Schrodinger equation | REGION | GUIDES | ANOMALOUS-DISPERSION | TRANSMISSION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | BISTABILITY | OPTICAL-FIBERS | INDEX CHANGE | WAVE-PROPAGATION

Solitary solutions | Non-linear SchrÃ¶dinger equation | Non-linear effects | Saturable soliton | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | COLLISION | PHYSICS, MATHEMATICAL | Non-linear Schrodinger equation | REGION | GUIDES | ANOMALOUS-DISPERSION | TRANSMISSION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | BISTABILITY | OPTICAL-FIBERS | INDEX CHANGE | WAVE-PROPAGATION

Journal Article

Physics Letters A, ISSN 0375-9601, 07/2016, Volume 380, Issue 33, pp. 2549 - 2560

In this paper flame instabilities are analyzed utilizing the Sivashinsky equation in order to derive the flame wrinkling factor. This is a synthetic variable...

Sivashinsky equation | Flame modeling | Flame acceleration | Hydrogen | Flame instability | PHYSICS, MULTIDISCIPLINARY | SELF-ACCELERATION | DISCONTINUITIES | NON-LINEAR ANALYSIS | FRONTS | PREMIXED FLAMES | DYNAMICS | SURFACE | LAMINAR FLAMES | HYDRODYNAMIC INSTABILITY | Analysis | Wrinkling | Stability | Mathematical analysis | Solid state physics | Instability | Mathematical models | Acceleration

Sivashinsky equation | Flame modeling | Flame acceleration | Hydrogen | Flame instability | PHYSICS, MULTIDISCIPLINARY | SELF-ACCELERATION | DISCONTINUITIES | NON-LINEAR ANALYSIS | FRONTS | PREMIXED FLAMES | DYNAMICS | SURFACE | LAMINAR FLAMES | HYDRODYNAMIC INSTABILITY | Analysis | Wrinkling | Stability | Mathematical analysis | Solid state physics | Instability | Mathematical models | Acceleration

Journal Article

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, ISSN 1751-8113, 09/2018, Volume 51, Issue 38, p. 385401

The massive ordinary differential equation/integrable model (ODE/IM) correspondence is a relation between the linear problem associated with modified affine...

PHYSICS, MULTIDISCIPLINARY | ODE/IM correspondence | DIFFERENTIAL-EQUATIONS | Q-OPERATORS | non-linear integral equation | FINITE-VOLUME SPECTRUM | PHYSICS, MATHEMATICAL | FUNCTIONAL RELATIONS | Bethe ansatz equation | MODELS | W algebra | T-Q relation | STOKES MULTIPLIERS | affine Toda field equation | THERMODYNAMIC BETHE-ANSATZ

PHYSICS, MULTIDISCIPLINARY | ODE/IM correspondence | DIFFERENTIAL-EQUATIONS | Q-OPERATORS | non-linear integral equation | FINITE-VOLUME SPECTRUM | PHYSICS, MATHEMATICAL | FUNCTIONAL RELATIONS | Bethe ansatz equation | MODELS | W algebra | T-Q relation | STOKES MULTIPLIERS | affine Toda field equation | THERMODYNAMIC BETHE-ANSATZ

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 5/2018, Volume 92, Issue 3, pp. 1103 - 1108

By utilizing the Hirotaâ€™s bilinear form and symbolic computation, abundant lump solutions and lumpâ€“kink solutions of the new (3Â +Â 1)-dimensional generalized...

Hirotaâ€™s bilinear form | Engineering | Vibration, Dynamical Systems, Control | Lumpâ€“kink solutions | Lump solutions | Classical Mechanics | Automotive Engineering | Mechanical Engineering | New generalized Kadomtsevâ€“Petviashvili equation | RATIONAL SOLUTIONS | WAVE | MECHANICS | Hirota's bilinear form | Lump-kink solutions | JIMBO-MIWA | New generalized Kadomtsev-Petviashvili equation | MULTIPLE-SOLITON-SOLUTIONS | ENGINEERING, MECHANICAL | Exponential functions

Hirotaâ€™s bilinear form | Engineering | Vibration, Dynamical Systems, Control | Lumpâ€“kink solutions | Lump solutions | Classical Mechanics | Automotive Engineering | Mechanical Engineering | New generalized Kadomtsevâ€“Petviashvili equation | RATIONAL SOLUTIONS | WAVE | MECHANICS | Hirota's bilinear form | Lump-kink solutions | JIMBO-MIWA | New generalized Kadomtsev-Petviashvili equation | MULTIPLE-SOLITON-SOLUTIONS | ENGINEERING, MECHANICAL | Exponential functions

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2019, Volume 476, Issue 1, pp. 53 - 85

We consider the problem of global in time existence and uniqueness for the initial value problems for scaling parameters and a large class of initial data ....

Stochastic multiplicative cascade | Branching processes | Non-uniqueness of solutions | Stochastic explosions | Stochastic recursion | Non-linear/non-local differential equations | MATHEMATICS | MATHEMATICS, APPLIED | UNIQUENESS

Stochastic multiplicative cascade | Branching processes | Non-uniqueness of solutions | Stochastic explosions | Stochastic recursion | Non-linear/non-local differential equations | MATHEMATICS | MATHEMATICS, APPLIED | UNIQUENESS

Journal Article

13.
Full Text
Pattern formation in a flux limited reactionâ€“diffusion equation of porous media type

Inventiones mathematicae, ISSN 0020-9910, 10/2016, Volume 206, Issue 1, pp. 57 - 108

A non-linear PDE featuring flux limitation effects together with those of the porous media equation (non-linear Fokkerâ€“Planck) is presented in this paper. We...

Primary 35K57 | 35B36 | 34Cxx | 76B15 | 37Dxx | 35Q99 | Mathematics | 70Kxx | 35K67 | 37D50 | 35Q35 | Mathematics, general | Secondary 35B60 | FISHER-KPP EQUATIONS | MATHEMATICS | POPULATION-GENETICS | FRONTS | COMBUSTION | NON-LINEAR DIFFUSION | CONSERVATION-LAWS | MODEL | BURGERS-TYPE EQUATIONS | PROPAGATION | TRAVELING-WAVES

Primary 35K57 | 35B36 | 34Cxx | 76B15 | 37Dxx | 35Q99 | Mathematics | 70Kxx | 35K67 | 37D50 | 35Q35 | Mathematics, general | Secondary 35B60 | FISHER-KPP EQUATIONS | MATHEMATICS | POPULATION-GENETICS | FRONTS | COMBUSTION | NON-LINEAR DIFFUSION | CONSERVATION-LAWS | MODEL | BURGERS-TYPE EQUATIONS | PROPAGATION | TRAVELING-WAVES

Journal Article

Engineering Analysis with Boundary Elements, ISSN 0955-7997, 2008, Volume 32, Issue 9, pp. 747 - 756

In this paper the meshless local Petrovâ€“Galerkin (MLPG) method is presented for the numerical solution of the two-dimensional non-linear SchrÃ¶dinger equation....

Unit Heaviside test function | Moving least square (MLS) approximation | Non-linear SchrÃ¶dinger equation | Meshless local Petrovâ€“Galerkin (MLPG) method | Meshless local Petrov-Galerkin (MLPG) method | non-linear Schrodinger equation | unit heaviside test function | BOUNDARY-CONDITIONS | PLATES | SIMULATION | meshless local Petrov-Galerkin (MLPG) method | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | SOLIDS | moving least square (MLS) approximation | SUBJECT | WAVE-EQUATION | RADIAL BASIS FUNCTIONS | HEAT-CONDUCTION | THICK | SCHEMES | Finite element method | Approximation | Mathematical analysis | Meshless methods | Nonlinearity | Mathematical models | Schroedinger equation | Two dimensional

Unit Heaviside test function | Moving least square (MLS) approximation | Non-linear SchrÃ¶dinger equation | Meshless local Petrovâ€“Galerkin (MLPG) method | Meshless local Petrov-Galerkin (MLPG) method | non-linear Schrodinger equation | unit heaviside test function | BOUNDARY-CONDITIONS | PLATES | SIMULATION | meshless local Petrov-Galerkin (MLPG) method | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | SOLIDS | moving least square (MLS) approximation | SUBJECT | WAVE-EQUATION | RADIAL BASIS FUNCTIONS | HEAT-CONDUCTION | THICK | SCHEMES | Finite element method | Approximation | Mathematical analysis | Meshless methods | Nonlinearity | Mathematical models | Schroedinger equation | Two dimensional

Journal Article

Computer Physics Communications, ISSN 0010-4655, 03/2017, Volume 212, pp. 269 - 279

Energetic electrons are of interest in many types of plasmas, however previous modeling of their properties has been restricted to the use of linear...

Kinetic plasma theory | Non-linear relativistic Fokkerâ€“Planck equation | Runaway electrons | Energetic electrons | ALGORITHM | COLLISION OPERATOR | PHYSICS, MATHEMATICAL | Non-linear relativistic Fokker-Planck equation | TOKAMAKS | DISTRIBUTIONS | ACCELERATION | AVALANCHE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ION RUNAWAY | FULLY IONIZED GAS | EMISSION | Analysis | Electrons | Magnetization | Physics - Plasma Physics | Fusion, Plasma and Space Physics | Fusion, plasma och rymdfysik

Kinetic plasma theory | Non-linear relativistic Fokkerâ€“Planck equation | Runaway electrons | Energetic electrons | ALGORITHM | COLLISION OPERATOR | PHYSICS, MATHEMATICAL | Non-linear relativistic Fokker-Planck equation | TOKAMAKS | DISTRIBUTIONS | ACCELERATION | AVALANCHE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ION RUNAWAY | FULLY IONIZED GAS | EMISSION | Analysis | Electrons | Magnetization | Physics - Plasma Physics | Fusion, Plasma and Space Physics | Fusion, plasma och rymdfysik

Journal Article

Geophysical Journal International, ISSN 0956-540X, 07/2018, Volume 214, Issue 1, pp. 58 - 69

The electrical potential at the interface between mineral and water is traditionally computed from the Poisson-Boltzmann (P-B) equation. Nevertheless, this...

Electrical properties | Non-linear differential equations | Hydrogeophysics | CLAY-MINERALS | ELECTROOSMOTIC FLOW | NANOFLUIDIC CHANNELS | GEOCHEMISTRY & GEOPHYSICS | OXIDE-WATER INTERFACE | ELECTROKINETIC PHENOMENA | COMPLEX CONDUCTIVITY | SPECTRAL INDUCED POLARIZATION | SURFACE-CHARGE DENSITY | TRIPLE-LAYER MODEL | MEMBRANE POLARIZATION | Physics | Geophysics

Electrical properties | Non-linear differential equations | Hydrogeophysics | CLAY-MINERALS | ELECTROOSMOTIC FLOW | NANOFLUIDIC CHANNELS | GEOCHEMISTRY & GEOPHYSICS | OXIDE-WATER INTERFACE | ELECTROKINETIC PHENOMENA | COMPLEX CONDUCTIVITY | SPECTRAL INDUCED POLARIZATION | SURFACE-CHARGE DENSITY | TRIPLE-LAYER MODEL | MEMBRANE POLARIZATION | Physics | Geophysics

Journal Article

Inventiones mathematicae, ISSN 0020-9910, 12/2006, Volume 166, Issue 3, pp. 645 - 675

We prove, for the energy critical, focusing NLS, that for data whose energy is smaller than that of the standing wave, and whose homogeneous Sobolev norm H^1...

Mathematics, general | Mathematics | EXISTENCE | MATHEMATICS | NON-LINEAR SCHRODINGER | MASS | CAUCHY-PROBLEM | CRITICAL POWER | TIME | COMPACTNESS | KLEIN-GORDON EQUATIONS | Mathematics - Analysis of PDEs

Mathematics, general | Mathematics | EXISTENCE | MATHEMATICS | NON-LINEAR SCHRODINGER | MASS | CAUCHY-PROBLEM | CRITICAL POWER | TIME | COMPACTNESS | KLEIN-GORDON EQUATIONS | Mathematics - Analysis of PDEs

Journal Article

18.
Full Text
Survey of State-Dependent Riccati Equation in Nonlinear Optimal Feedback Control Synthesis

Journal of Guidance, Control, and Dynamics, ISSN 0731-5090, 07/2012, Volume 35, Issue 4, pp. 1025 - 1047

Â Tayfun Ã‡imen is a Control Engineering Scientist. He received a B.Eng. with first-class honors in computer systems engineering in 2000 and a Ph.D. in systems...

INSTRUMENTS & INSTRUMENTATION | UNCERTAIN SYSTEMS | H-INFINITY-CONTROL | NON-LINEAR SYSTEMS | STABILIZING FEEDBACK | INTEGRATED GUIDANCE | HAMILTON-JACOBI EQUATIONS | AEROELASTIC SYSTEM | DYNAMICAL SYSTEMS | ENGINEERING, AEROSPACE | SUBOPTIMAL CONTROL | ANGULAR-RATE ESTIMATION | Nonlinear dynamics | Aircraft components | Aerospace | Optimal control | Control systems | Nonlinearity | Trajectories | Control theory

INSTRUMENTS & INSTRUMENTATION | UNCERTAIN SYSTEMS | H-INFINITY-CONTROL | NON-LINEAR SYSTEMS | STABILIZING FEEDBACK | INTEGRATED GUIDANCE | HAMILTON-JACOBI EQUATIONS | AEROELASTIC SYSTEM | DYNAMICAL SYSTEMS | ENGINEERING, AEROSPACE | SUBOPTIMAL CONTROL | ANGULAR-RATE ESTIMATION | Nonlinear dynamics | Aircraft components | Aerospace | Optimal control | Control systems | Nonlinearity | Trajectories | Control theory

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 2019, Volume 52, Issue 3, p. 35202

We investigate dispersive and Strichartz estimates for the Schrodinger time evolution propagator e(-itH) on a star-shaped metric graph. The linear operator, H,...

Schrodinger operator | quantum graphs | Strichartz estimates | non- linear Schrodinger equation | dispersion | LAPLACIANS | NETWORK | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | QUANTUM GRAPH | THIN FIBERS

Schrodinger operator | quantum graphs | Strichartz estimates | non- linear Schrodinger equation | dispersion | LAPLACIANS | NETWORK | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | QUANTUM GRAPH | THIN FIBERS

Journal Article