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

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 Jacobi–Gauss–Lobatto collocation method for solving the generalized Fitzhugh–Nagumo equation. The Jacobi–Gauss–Lobatto points...

Generalized Fitzhugh–Nagumo equation | Real Newell–Whitehead equation | Time-dependent Fitzhugh–Nagumo equation | Collocation method | Implicit Runge–Kutta method | Jacobi–Gauss–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 Fitzhugh–Nagumo equation | Real Newell–Whitehead equation | Time-dependent Fitzhugh–Nagumo equation | Collocation method | Implicit Runge–Kutta method | Jacobi–Gauss–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 | Reaction–diffusion equation | Navier–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 | Reaction–diffusion equation | Navier–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 Allen–Cahn equation in one-dimensional Euclidean space. This equation is a scalar reaction–diffusion equation...

Entire solution | Super–sub-solutions | Reaction–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 | Super–sub-solutions | Reaction–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 Schrödinger equation for optical medias with saturable non-linear refractive index is obtained and numerical calculation method is applied and...

Solitary solutions | Non-linear Schrödinger 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 Schrödinger 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

8.
Full Text
An analysis of flame instabilities for hydrogen–air mixtures based on Sivashinsky equation

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 Hirota’s bilinear form and symbolic computation, abundant lump solutions and lump–kink solutions of the new (3 + 1)-dimensional generalized...

Hirota’s bilinear form | Engineering | Vibration, Dynamical Systems, Control | Lump–kink solutions | Lump solutions | Classical Mechanics | Automotive Engineering | Mechanical Engineering | New generalized Kadomtsev–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

Hirota’s bilinear form | Engineering | Vibration, Dynamical Systems, Control | Lump–kink solutions | Lump solutions | Classical Mechanics | Automotive Engineering | Mechanical Engineering | New generalized Kadomtsev–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

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 Fokker–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 Petrov–Galerkin (MLPG) method is presented for the numerical solution of the two-dimensional non-linear Schrödinger equation....

Unit Heaviside test function | Moving least square (MLS) approximation | Non-linear Schrödinger equation | Meshless local Petrov–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 Schrödinger equation | Meshless local Petrov–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 Fokker–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 Fokker–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

17.
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

Tayfun Çimen 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

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 03/2018, Volume 474, Issue 2211, pp. 20170687 - 20170687

A Kuramoto-Sivashinsky equation in two space dimensions arising in thin film flows is considered on doubly periodic domains. In the absence of dispersive...

Active dissipative-dispersive nonlinear PDE | Spatio-temporal chaos | Kuramoto-Sivashinsky equation | THIN-FILMS | 2-DIMENSIONAL WAVE DYNAMICS | STABILITY | MULTIDISCIPLINARY SCIENCES | NON-LINEAR ANALYSIS | spatio-temporal chaos | STATIONARY SOLITARY PULSES | active dissipative-dispersive nonlinear PDE | BOUNDS | LAMINAR FLAMES | SYSTEMS | HYDRODYNAMIC INSTABILITY | SURFACES | Dynamic structural analysis | Nonlinear dynamics | Traveling waves | Flux density | Formulas (mathematics) | Dynamical systems | 1008 | active dissipative–dispersive nonlinear PDE | Kuramoto–Sivashinsky equation

Active dissipative-dispersive nonlinear PDE | Spatio-temporal chaos | Kuramoto-Sivashinsky equation | THIN-FILMS | 2-DIMENSIONAL WAVE DYNAMICS | STABILITY | MULTIDISCIPLINARY SCIENCES | NON-LINEAR ANALYSIS | spatio-temporal chaos | STATIONARY SOLITARY PULSES | active dissipative-dispersive nonlinear PDE | BOUNDS | LAMINAR FLAMES | SYSTEMS | HYDRODYNAMIC INSTABILITY | SURFACES | Dynamic structural analysis | Nonlinear dynamics | Traveling waves | Flux density | Formulas (mathematics) | Dynamical systems | 1008 | active dissipative–dispersive nonlinear PDE | Kuramoto–Sivashinsky equation

Journal Article