Pramana, ISSN 0304-4289, 5/2018, Volume 90, Issue 5, pp. 1 - 20

In this research, we apply two different techniques on nonlinear complex fractional nonlinear Schrödinger equation which is a very important model in...

new auxiliary equation method | optical solitary travelling wave solutions | Astrophysics and Astroparticles | novel $$\left( {G'}/{G}\right) $$ G ′ / G -expansion method | kink and antikink | Physics, general | Nonlinear complex fractional Schrödinger equation | Physics | Astronomy, Observations and Techniques | novel (G | G) -expansion method | BOUSSINESQ EQUATION | PHYSICS, MULTIDISCIPLINARY | BIFURCATIONS | novel (G '/G)-expansion method | FIBERS | TRAVELING-WAVE SOLUTIONS | EVOLUTION | Nonlinear complex fractional Schrodinger equation | GINZBURG-LANDAU EQUATION | BRIGHT | Quantum theory | Methods

new auxiliary equation method | optical solitary travelling wave solutions | Astrophysics and Astroparticles | novel $$\left( {G'}/{G}\right) $$ G ′ / G -expansion method | kink and antikink | Physics, general | Nonlinear complex fractional Schrödinger equation | Physics | Astronomy, Observations and Techniques | novel (G | G) -expansion method | BOUSSINESQ EQUATION | PHYSICS, MULTIDISCIPLINARY | BIFURCATIONS | novel (G '/G)-expansion method | FIBERS | TRAVELING-WAVE SOLUTIONS | EVOLUTION | Nonlinear complex fractional Schrodinger equation | GINZBURG-LANDAU EQUATION | BRIGHT | Quantum theory | Methods

Journal Article

1999, Applied mathematical sciences, ISBN 9780387986111, Volume 139., XVI, 350

eBook

Journal of Modern Optics, ISSN 0950-0340, 11/2013, Volume 60, Issue 19, pp. 1627 - 1636

In this paper, the resonant nonlinear Schrödinger's equation is studied with four forms of nonlinearity. This equation is also considered with time-dependent...

integrability | solitons | Integrability | Solitons | MKDV EQUATION | DIFFERENTIAL-EQUATIONS | WAVE SOLUTIONS | OPTICS | SUB-ODE METHOD | VARIABLE-COEFFICIENT | Optical fibers | Mathematical analysis | Nonlinear evolution equations | Tools | Nonlinearity | Schroedinger equation

integrability | solitons | Integrability | Solitons | MKDV EQUATION | DIFFERENTIAL-EQUATIONS | WAVE SOLUTIONS | OPTICS | SUB-ODE METHOD | VARIABLE-COEFFICIENT | Optical fibers | Mathematical analysis | Nonlinear evolution equations | Tools | Nonlinearity | Schroedinger equation

Journal Article

1999, IAS/Park City mathematics series, ISBN 9780821805923, Volume 5, xii, 466

Book

Annals of Physics, ISSN 0003-4916, 02/2014, Volume 341, pp. 142 - 152

The one-to-one correspondence between a -dimensional variable-coefficient nonlinear Schrödinger equation with linear and parabolic potentials and a standard...

Superposed Akhmediev breather | Controllable dynamical behaviors | Nonlinear Schrödinger equation | PHYSICS, MULTIDISCIPLINARY | Nonlinear Schrodinger equation | ROGUE WAVES | FIBER | SOLITONS | PLASMA | MODULATION INSTABILITY | SOLITARY WAVES | DYNAMICS | LATTICES | SCATTERING | Chirp | Diffraction | Nonlinearity | Controllability | Evolution | Schroedinger equation | Terminals | Gain | MATHEMATICAL SOLUTIONS | EXCITATION | PEAKS | NONLINEAR PROBLEMS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | EQUATIONS | DIFFRACTION | AMPLITUDES | POTENTIALS | GAIN

Superposed Akhmediev breather | Controllable dynamical behaviors | Nonlinear Schrödinger equation | PHYSICS, MULTIDISCIPLINARY | Nonlinear Schrodinger equation | ROGUE WAVES | FIBER | SOLITONS | PLASMA | MODULATION INSTABILITY | SOLITARY WAVES | DYNAMICS | LATTICES | SCATTERING | Chirp | Diffraction | Nonlinearity | Controllability | Evolution | Schroedinger equation | Terminals | Gain | MATHEMATICAL SOLUTIONS | EXCITATION | PEAKS | NONLINEAR PROBLEMS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | EQUATIONS | DIFFRACTION | AMPLITUDES | POTENTIALS | GAIN

Journal Article

Optics Letters, ISSN 0146-9592, 03/2015, Volume 40, Issue 6, pp. 1117 - 1120

In quantum mechanics, the space-fractional Schrodinger equation provides a natural extension of the standard Schrodinger equation when the Brownian...

IMPLEMENTATION | OPTICS | QUANTUM-MECHANICS | OSCILLATOR | AIRY BEAM | LASER | Integrals | Dynamics | Quantum mechanics | Holes | Optical pumping | Schroedinger equation | Laser beams | Standards

IMPLEMENTATION | OPTICS | QUANTUM-MECHANICS | OSCILLATOR | AIRY BEAM | LASER | Integrals | Dynamics | Quantum mechanics | Holes | Optical pumping | Schroedinger equation | Laser beams | Standards

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 12/2015, Volume 82, Issue 4, pp. 1775 - 1780

In this paper, we establish exact soliton solutions for the Davey–Stewartson equation. The trial equation method and the ansatz approach are used to construct...

Davey–Stewartson equation | Engineering | Vibration, Dynamical Systems, Control | Ansatz approach | Mechanics | Trial equation method | Automotive Engineering | Mechanical Engineering | Davey-Stewartson equation | TRAVELING-WAVE SOLUTIONS | MECHANICS | 1-SOLITON SOLUTION | ENGINEERING, MECHANICAL | Solitary waves | Schroedinger equation

Davey–Stewartson equation | Engineering | Vibration, Dynamical Systems, Control | Ansatz approach | Mechanics | Trial equation method | Automotive Engineering | Mechanical Engineering | Davey-Stewartson equation | TRAVELING-WAVE SOLUTIONS | MECHANICS | 1-SOLITON SOLUTION | ENGINEERING, MECHANICAL | Solitary waves | Schroedinger equation

Journal Article

1992, ISBN 0195071573, xi, 494

Book

International Journal of Modern Physics D, ISSN 0218-2718, 04/2018, Volume 27, Issue 6, p. 1841004

The Wheeler–DeWitt equation was proposed 50 years ago and until now it is the cornerstone of most approaches to quantization of gravity. One can find in the...

extended phase space | quantum gravity | The Wheeler-DeWitt equation | EXTENDED PHASE-SPACE | FORMULATION | GRAVITY | RELATIVISTIC SYSTEMS | IX MODEL | ASTRONOMY & ASTROPHYSICS | HAMILTONIAN-DYNAMICS | CONSTRAINTS | QUANTIZATION | UNIVERSE | QUANTUM GEOMETRODYNAMICS

extended phase space | quantum gravity | The Wheeler-DeWitt equation | EXTENDED PHASE-SPACE | FORMULATION | GRAVITY | RELATIVISTIC SYSTEMS | IX MODEL | ASTRONOMY & ASTROPHYSICS | HAMILTONIAN-DYNAMICS | CONSTRAINTS | QUANTIZATION | UNIVERSE | QUANTUM GEOMETRODYNAMICS

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 11/2018, Volume 94, Issue 3, pp. 1921 - 1932

We use the method of multiple scales to derive a sixth-order nonlinear Schrödinger equation governing the evolution of slowly modulated plane-wave solutions to...

Engineering | Vibration, Dynamical Systems, Control | Nonlinear Klein–Gordon equation | Method of multiple scales | Nonlinear dispersion | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Nonlinear Schrödinger equation | Envelope | Multiple-scale analysis | PERIODIC-SOLUTIONS | INTEGRABILITY | ENVELOPE SOLITONS | Nonlinear Schrodinger equation | UNIFORM EXPANSIONS | ENGINEERING, MECHANICAL | MECHANICS | EVOLUTION | FLUID | DYNAMICS | SURFACE | SINE-GORDON | Nonlinear Klein-Gordon equation

Engineering | Vibration, Dynamical Systems, Control | Nonlinear Klein–Gordon equation | Method of multiple scales | Nonlinear dispersion | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Nonlinear Schrödinger equation | Envelope | Multiple-scale analysis | PERIODIC-SOLUTIONS | INTEGRABILITY | ENVELOPE SOLITONS | Nonlinear Schrodinger equation | UNIFORM EXPANSIONS | ENGINEERING, MECHANICAL | MECHANICS | EVOLUTION | FLUID | DYNAMICS | SURFACE | SINE-GORDON | Nonlinear Klein-Gordon equation

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 09/2019, Volume 186, pp. 209 - 218

This paper is concerned with an existence and stability result on the nonlinear derivative Schrödinger equation in 1-D, which is originated by the study of the...

SYSTEM | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | ENERGY WEAK SOLUTIONS | WELL-POSEDNESS | MODEL | Fluid dynamics | Operators (mathematics) | Fluid mechanics | Compressibility | Stability | Computational fluid dynamics | Nonlinear analysis | Fluid flow | Hydrodynamics | Schroedinger equation | Euler-Lagrange equation | Steady state

SYSTEM | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | ENERGY WEAK SOLUTIONS | WELL-POSEDNESS | MODEL | Fluid dynamics | Operators (mathematics) | Fluid mechanics | Compressibility | Stability | Computational fluid dynamics | Nonlinear analysis | Fluid flow | Hydrodynamics | Schroedinger equation | Euler-Lagrange equation | Steady state

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2012, Volume 218, Issue 10, pp. 5966 - 5973

The repeated homogeneous balance is used to construct a new exact traveling wave solution of the Kadomtsev–Petviashvili (KP) like equation coupled to a...

Homogeneous balance method | Soliton solutions | Kadomtsev–Petviashvili (KP) like equation coupled to a Schrödinger equation | Riccati equation | Traveling wave solutions | Kadomtsev-Petviashvili (KP) like equation coupled to a Schrödinger equation | SYSTEM | MATHEMATICS, APPLIED | Kadomtsev-Petviashvili (KP) like equation coupled to a Schrodinger equation | BACKLUND TRANSFORMATION | BOUSSINESQ-BURGERS EQUATIONS | TRAVELING-WAVE SOLUTIONS | NONLINEAR EQUATIONS | DE-VRIES EQUATIONS | KDV EQUATION | ALGEBRAIC-METHOD | Differential equations | Mathematical analysis | Solitons | Nonlinear evolution equations | Traveling waves | Mathematical models | Schroedinger equation

Homogeneous balance method | Soliton solutions | Kadomtsev–Petviashvili (KP) like equation coupled to a Schrödinger equation | Riccati equation | Traveling wave solutions | Kadomtsev-Petviashvili (KP) like equation coupled to a Schrödinger equation | SYSTEM | MATHEMATICS, APPLIED | Kadomtsev-Petviashvili (KP) like equation coupled to a Schrodinger equation | BACKLUND TRANSFORMATION | BOUSSINESQ-BURGERS EQUATIONS | TRAVELING-WAVE SOLUTIONS | NONLINEAR EQUATIONS | DE-VRIES EQUATIONS | KDV EQUATION | ALGEBRAIC-METHOD | Differential equations | Mathematical analysis | Solitons | Nonlinear evolution equations | Traveling waves | Mathematical models | Schroedinger equation

Journal Article

International Journal of Control, ISSN 0020-7179, 02/2019, Volume 92, Issue 2, pp. 416 - 430

In this work, we study the dynamic behaviour for a heat equation with exponential polynomial kernel memory to be a controller for a Schrödinger system. By...

heat equation with memory | asymptotic analysis | spectrum | Schrödinger equation | Riesz basis | exponential stability | Schrodinger equation | REGULARITY | CONTROLLABILITY | AUTOMATION & CONTROL SYSTEMS | Thermodynamics | Schroedinger equation | Eigenvectors | Polynomials | Feedback control | Markov analysis

heat equation with memory | asymptotic analysis | spectrum | Schrödinger equation | Riesz basis | exponential stability | Schrodinger equation | REGULARITY | CONTROLLABILITY | AUTOMATION & CONTROL SYSTEMS | Thermodynamics | Schroedinger equation | Eigenvectors | Polynomials | Feedback control | Markov analysis

Journal Article

Pramana, ISSN 0304-4289, 7/2019, Volume 93, Issue 1, pp. 1 - 3

This comment deals with the new auxiliary equation method (Khater method) introduced by Mostafa M A Khater, Aly R Seadawy and Dianchen Lu in Pramana – J. Phys....

Doubtful Khater method | Astrophysics and Astroparticles | doubtful exact solutions | amended Khater method | Physics, general | Physics | Astronomy, Observations and Techniques

Doubtful Khater method | Astrophysics and Astroparticles | doubtful exact solutions | amended Khater method | Physics, general | Physics | Astronomy, Observations and Techniques

Journal Article

15.
Full Text
Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation

Nonlinearity, ISSN 0951-7715, 02/2016, Volume 29, Issue 3, pp. 915 - 946

A nonlocal nonlinear Schrodinger (NLS) equation was recently introduced and shown to be an integrable infinite dimensional Hamiltonian evolution equation. In...

left-right Riemann-Hilbert problem | integrable nonlocal NLS equation | PT symmetry | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Inverse scattering | Mathematical analysis | Transforms | Solitons | Nonlinearity | Evolution | Schroedinger equation | Cauchy problem

left-right Riemann-Hilbert problem | integrable nonlocal NLS equation | PT symmetry | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Inverse scattering | Mathematical analysis | Transforms | Solitons | Nonlinearity | Evolution | Schroedinger equation | Cauchy problem

Journal Article

New Journal of Physics, ISSN 1367-2630, 11/2014, Volume 16, Issue 11, pp. 115007 - 17

The necessity of quantising the gravitational field is still subject to an open debate. In this paper we compare the approach of quantum gravity, with that of...

semi-classical gravity | collapse of the wave-function | Schrödinger-Newton equation | LOCALIZATION | QUANTUM STATE REDUCTION | PHYSICS, MULTIDISCIPLINARY | FIELD | Schrodinger-Newton equation | GRAVITY | VIOLATION | MECHANICS | COLLAPSE | SYSTEMS | DYNAMICAL REDUCTION MODELS | RELATIVITY | Collapse | Gravitation | Mathematical analysis | Nonlinearity | Mathematical models | Schroedinger equation | Signalling | Quantum gravity

semi-classical gravity | collapse of the wave-function | Schrödinger-Newton equation | LOCALIZATION | QUANTUM STATE REDUCTION | PHYSICS, MULTIDISCIPLINARY | FIELD | Schrodinger-Newton equation | GRAVITY | VIOLATION | MECHANICS | COLLAPSE | SYSTEMS | DYNAMICAL REDUCTION MODELS | RELATIVITY | Collapse | Gravitation | Mathematical analysis | Nonlinearity | Mathematical models | Schroedinger equation | Signalling | Quantum gravity

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 2018, Volume 95, Issue 2, pp. 983 - 994

Interactions of bright solitons in the Heisenberg ferromagnetic spin chain, governed by a (2+1)-dimensional nonlinear Schrodinger equation with variable...

Variable-coefficient nonlinear Schrödinger equation | Soliton interaction | Heisenberg ferromagnetic spin chain | Soliton propagation | MECHANICS | CUBIC NONLINEARITY | Variable-coefficient nonlinear Schrodinger equation | PERTURBATION | QUARTIC OPTICAL SOLITONS | KERR | CONSERVATION-LAWS | COLLISIONS | ENGINEERING, MECHANICAL | Ferromagnetism

Variable-coefficient nonlinear Schrödinger equation | Soliton interaction | Heisenberg ferromagnetic spin chain | Soliton propagation | MECHANICS | CUBIC NONLINEARITY | Variable-coefficient nonlinear Schrodinger equation | PERTURBATION | QUARTIC OPTICAL SOLITONS | KERR | CONSERVATION-LAWS | COLLISIONS | ENGINEERING, MECHANICAL | Ferromagnetism

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 01/2012, Volume 57, Issue 1, pp. 179 - 185

We study stability of a Schrödinger equation with a collocated boundary feedback compensator in the form of a heat equation with a collocated input/output...

Asymptotic stability | Heating | Eigenvalues and eigenfunctions | Gevrey class | Equations | Numerical stability | Manganese | Aerospace engineering | BEAM | OPERATORS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Boundary value problems | Usage | Analysis | Feedback control systems | Series, Taylor's | Innovations | Eigenvalues | Evolutionary algorithms | Stability | Asymptotic properties | Feedback | Control systems | Schroedinger equation | Boundaries | Control theory | Heat equations

Asymptotic stability | Heating | Eigenvalues and eigenfunctions | Gevrey class | Equations | Numerical stability | Manganese | Aerospace engineering | BEAM | OPERATORS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Boundary value problems | Usage | Analysis | Feedback control systems | Series, Taylor's | Innovations | Eigenvalues | Evolutionary algorithms | Stability | Asymptotic properties | Feedback | Control systems | Schroedinger equation | Boundaries | Control theory | Heat equations

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 4/2017, Volume 88, Issue 2, pp. 1257 - 1271

The Darboux transformation (DT) for the super-integrable hierarchy has an essential difference from the general system. As we know, the super-integrable...

Super-Dirac equation | Engineering | Vibration, Dynamical Systems, Control | Super-Schrödinger equation | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Darboux transformation | Exact solution | SUPERSYMMETRIES | INTEGRABILITY | NONLINEAR-WAVES | SYMMETRIES | HARMONIC-OSCILLATOR | Super-Schrodinger equation | EVOLUTION-EQUATIONS | ENGINEERING, MECHANICAL | MECHANICS | VARIABLE-COEFFICIENTS | SOLITON-SOLUTIONS | OPERATOR | HIERARCHY | Inhomogeneous media | Transformations | Schroedinger equation | Hierarchies | Solitary waves | Dirac equation

Super-Dirac equation | Engineering | Vibration, Dynamical Systems, Control | Super-Schrödinger equation | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Darboux transformation | Exact solution | SUPERSYMMETRIES | INTEGRABILITY | NONLINEAR-WAVES | SYMMETRIES | HARMONIC-OSCILLATOR | Super-Schrodinger equation | EVOLUTION-EQUATIONS | ENGINEERING, MECHANICAL | MECHANICS | VARIABLE-COEFFICIENTS | SOLITON-SOLUTIONS | OPERATOR | HIERARCHY | Inhomogeneous media | Transformations | Schroedinger equation | Hierarchies | Solitary waves | Dirac equation

Journal Article

PLoS ONE, ISSN 1932-6203, 02/2018, Volume 13, Issue 2, p. e0192281

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear...

FERROMAGNETIC SPIN CHAIN | TRANSFORMATION | EXISTENCE | RATIONAL SOLUTIONS | MULTIDISCIPLINARY SCIENCES | BREATHERS | SOLITARY SOLUTIONS | Singularities | Partial differential equations | Optics | Waves | Optical waveguides | Information science | Mathematical analysis | Klein-Gordon equation | Schroedinger equation | Mathematical models | Solitary waves | Symmetry | Breathers

FERROMAGNETIC SPIN CHAIN | TRANSFORMATION | EXISTENCE | RATIONAL SOLUTIONS | MULTIDISCIPLINARY SCIENCES | BREATHERS | SOLITARY SOLUTIONS | Singularities | Partial differential equations | Optics | Waves | Optical waveguides | Information science | Mathematical analysis | Klein-Gordon equation | Schroedinger equation | Mathematical models | Solitary waves | Symmetry | Breathers

Journal Article