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

Modern Physics Letters B, ISSN 0217-9849, 10/2017, Volume 31, Issue 29, p. 1750269

High-order rogue wave solutions of the Benjamin–Ono equation and the nonlocal nonlinear Schrödinger equation are derived by employing the bilinear method,...

Bilinear method | Rogue waves | Benjamin-Ono equation | Nonlocal nonlinear Schrödinger equation | nonlocal nonlinear Schrodinger equation | RATIONAL SOLUTIONS | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | SOLITON-SOLUTIONS | NLS | DYNAMICS | rogue waves | bilinear method | PHYSICS, MATHEMATICAL

Bilinear method | Rogue waves | Benjamin-Ono equation | Nonlocal nonlinear Schrödinger equation | nonlocal nonlinear Schrodinger equation | RATIONAL SOLUTIONS | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | SOLITON-SOLUTIONS | NLS | DYNAMICS | rogue waves | bilinear method | PHYSICS, MATHEMATICAL

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 10/2019, Volume 98, Issue 1, pp. 359 - 374

We use Whitham’s averaged Lagrangian method extended with the multiple-scale formalism to derive a sixth-order nonlinear Schrödinger equation for the complex...

Method of multiple scales | Nonlinear dispersion | Classical Mechanics | Quasi-soliton | Envelope | Averaged Lagrangian | Engineering | Vibration, Dynamical Systems, Control | Nonlinear Klein–Gordon equation | Sine-Gordon equation | Automotive Engineering | Mechanical Engineering | Nonlinear Schrödinger equation

Method of multiple scales | Nonlinear dispersion | Classical Mechanics | Quasi-soliton | Envelope | Averaged Lagrangian | Engineering | Vibration, Dynamical Systems, Control | Nonlinear Klein–Gordon equation | Sine-Gordon equation | Automotive Engineering | Mechanical Engineering | Nonlinear Schrödinger equation

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 7/2016, Volume 85, Issue 2, pp. 813 - 816

This paper applied the trial solution technique to chiral nonlinear Schrodinger’s equation in (1 $$+$$ + 2)-dimensions. This led to solitons and other...

Chiral NLSE | Engineering | Vibration, Dynamical Systems, Control | Solitons and singular periodic solutions | Mechanics | Trial solution technique | Automotive Engineering | Mechanical Engineering | Solitary waves | Nonlinear equations | Schroedinger equation

Chiral NLSE | Engineering | Vibration, Dynamical Systems, Control | Solitons and singular periodic solutions | Mechanics | Trial solution technique | Automotive Engineering | Mechanical Engineering | Solitary waves | Nonlinear equations | Schroedinger equation

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 05/2016, Volume 84, Issue 3, pp. 1157 - 1161

To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s11071-015-2560-9

Spatiotemporal Hermite–Gaussian solitons | Nonlinear Schrödinger equation | Partially nonlocal nonlinearity | Gaussian processes | Solitary waves | Schroedinger equation | Nonlinear dynamics | Nonlinearity | Approximation | Solitons

Spatiotemporal Hermite–Gaussian solitons | Nonlinear Schrödinger equation | Partially nonlocal nonlinearity | Gaussian processes | Solitary waves | Schroedinger equation | Nonlinear dynamics | Nonlinearity | Approximation | Solitons

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 05/2016, Volume 71, Issue 10, pp. 2001 - 2007

In this paper, a ( )-dimensional nonlinear Schrödinger equation for a ( )-dimensional Heisenberg ferromagnetic spin chain with the bilinear and anisotropic...

Multi-soliton solutions | Soliton interaction | Nonlinear Schrödinger equation | Heisenberg ferromagnetic spin chain | CHAIN | MATHEMATICS, APPLIED | SOLITON SPIN EXCITATIONS | Nonlinear Schrodinger equation | Anisotropy | Analysis | Ferromagnetism | Asymptotic properties | Mathematical analysis | Solitons | Nonlinearity | Mathematical models | Schroedinger equation | Invariants

Multi-soliton solutions | Soliton interaction | Nonlinear Schrödinger equation | Heisenberg ferromagnetic spin chain | CHAIN | MATHEMATICS, APPLIED | SOLITON SPIN EXCITATIONS | Nonlinear Schrodinger equation | Anisotropy | Analysis | Ferromagnetism | Asymptotic properties | Mathematical analysis | Solitons | Nonlinearity | Mathematical models | Schroedinger equation | Invariants

Journal Article

27.
Full Text
General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation

Proceedings: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 6/2012, Volume 468, Issue 2142, pp. 1716 - 1740

General high-order rogue waves in the nonlinear Schrödinger equation are derived by the bilinear method. These rogue waves are given in terms of determinants...

Amplitude | Algebra | Solitons | Determinants | Polynomials | Coefficients | Waves | Algebraic conjugates | Mathematical expressions | Bilinear method | Rogue waves | Nonlinear Schrödinger equation | FIBER | NLS EQUATION | SOLITONS | MULTIDISCIPLINARY SCIENCES | nonlinear Schrodinger equation | rogue waves | bilinear method | PULSES | Amplitudes | Dynamics | Mathematical analysis | Nonlinearity | Schroedinger equation | Arrays

Amplitude | Algebra | Solitons | Determinants | Polynomials | Coefficients | Waves | Algebraic conjugates | Mathematical expressions | Bilinear method | Rogue waves | Nonlinear Schrödinger equation | FIBER | NLS EQUATION | SOLITONS | MULTIDISCIPLINARY SCIENCES | nonlinear Schrodinger equation | rogue waves | bilinear method | PULSES | Amplitudes | Dynamics | Mathematical analysis | Nonlinearity | Schroedinger equation | Arrays

Journal Article

Physical Review Letters, ISSN 0031-9007, 10/2015, Volume 115, Issue 18, p. 180403

The dynamics of wave packets in the fractional Schrodinger equation is still an open problem. The difficulty stems from the fact that the fractional Laplacian...

RELATIVISTIC HARMONIC-OSCILLATOR | SOLITONS | PHYSICS, MULTIDISCIPLINARY | FLOQUET TOPOLOGICAL INSULATORS | MEDIA | POTENTIALS | QUANTUM-MECHANICS | BOSE-EINSTEIN CONDENSATION | Harmonics | Beams (radiation) | Gaussian beams (optics) | Dynamics | Schroedinger equation | Derivatives | Two dimensional | Stems

RELATIVISTIC HARMONIC-OSCILLATOR | SOLITONS | PHYSICS, MULTIDISCIPLINARY | FLOQUET TOPOLOGICAL INSULATORS | MEDIA | POTENTIALS | QUANTUM-MECHANICS | BOSE-EINSTEIN CONDENSATION | Harmonics | Beams (radiation) | Gaussian beams (optics) | Dynamics | Schroedinger equation | Derivatives | Two dimensional | Stems

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 07/2018, Volume 93, Issue 2, pp. 721 - 731

We investigate a -dimensional nonlocal nonlinear Schrodinger equation with the self-induced parity-time symmetric potential. By employing the Hirota's bilinear...

Hirota’s bilinear method | Soliton solution | KP hierarchy reduction method | (2 + 1) -Dimensional nonlocal nonlinear Schrödinger | TRANSFORMATION | MECHANICS | (2+1)-Dimensional nonlocal nonlinear Schrodinger equation | Hirota's bilinear method | DIFFERENTIAL-EQUATION | DYNAMICS | MEDIA | MODULATION | ENGINEERING, MECHANICAL | ROGUE WAVES | Information science | Boundary conditions | Solitary waves | Schroedinger equation

Hirota’s bilinear method | Soliton solution | KP hierarchy reduction method | (2 + 1) -Dimensional nonlocal nonlinear Schrödinger | TRANSFORMATION | MECHANICS | (2+1)-Dimensional nonlocal nonlinear Schrodinger equation | Hirota's bilinear method | DIFFERENTIAL-EQUATION | DYNAMICS | MEDIA | MODULATION | ENGINEERING, MECHANICAL | ROGUE WAVES | Information science | Boundary conditions | Solitary waves | Schroedinger equation

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 10/2015, Volume 299, pp. 1 - 21

In this study we aim to solve the cubic nonlinear Schrödinger (CNLS) equation by the method of fractional steps. Over a time step from to , the linear part of...

Explicit symplectic scheme | Method of fractional steps | Four temporal steps | Dispersion relation equation | Cubic Schrödinger equation | NUMERICAL-METHODS | INSTABILITY | DIFFERENCE-SCHEMES | PHYSICS, MATHEMATICAL | HAMILTONIAN PDES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SYSTEMS | MULTI-SYMPLECTIC METHODS | Cubic Schrodinger equation | INTEGRATORS | SEMICLASSICAL LIMIT | Computer simulation | Computation | Mathematical analysis | Nonlinearity | Mathematical models | Schroedinger equation | Dispersions | Derivatives

Explicit symplectic scheme | Method of fractional steps | Four temporal steps | Dispersion relation equation | Cubic Schrödinger equation | NUMERICAL-METHODS | INSTABILITY | DIFFERENCE-SCHEMES | PHYSICS, MATHEMATICAL | HAMILTONIAN PDES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SYSTEMS | MULTI-SYMPLECTIC METHODS | Cubic Schrodinger equation | INTEGRATORS | SEMICLASSICAL LIMIT | Computer simulation | Computation | Mathematical analysis | Nonlinearity | Mathematical models | Schroedinger equation | Dispersions | Derivatives

Journal Article

The Journal of Chemical Physics, ISSN 0021-9606, 12/2018, Volume 149, Issue 24, p. 244116

The free-complement (FC) theory for solving the Schrödinger equation (SE) was applied to calculate the potential energy curves of the ground and excited states...

Potential energy | Negative ions | Mathematical analysis | Hydrogen | Angular momentum | Atomic states | Schroedinger equation

Potential energy | Negative ions | Mathematical analysis | Hydrogen | Angular momentum | Atomic states | Schroedinger equation

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 1/2016, Volume 83, Issue 1, pp. 731 - 738

This paper addresses soliton propagation through optical fibers by the aid of Biswas–Milovic equation that serves as a generalized version of the usual...

Engineering | Vibration, Dynamical Systems, Control | Biswas–Milovic equation | Integrability | Optical solitons | Mechanics | Automotive Engineering | Mechanical Engineering | SINE-COSINE METHOD | DISPERSION | SCHRODINGERS EQUATION | EVOLUTION-EQUATIONS | ENGINEERING, MECHANICAL | (G'/G)-EXPANSION METHOD | PERTURBATION-THEORY | FIBERS | TRAVELING-WAVE SOLUTIONS | MECHANICS | KERR | TOPOLOGICAL 1-SOLITON SOLUTION | Biswas-Milovic equation | Optical fibers | Schroedinger equation | Power law | Solitary waves | Mathematical analysis | Solitons | Nonlinearity | Mathematical models | Cases

Engineering | Vibration, Dynamical Systems, Control | Biswas–Milovic equation | Integrability | Optical solitons | Mechanics | Automotive Engineering | Mechanical Engineering | SINE-COSINE METHOD | DISPERSION | SCHRODINGERS EQUATION | EVOLUTION-EQUATIONS | ENGINEERING, MECHANICAL | (G'/G)-EXPANSION METHOD | PERTURBATION-THEORY | FIBERS | TRAVELING-WAVE SOLUTIONS | MECHANICS | KERR | TOPOLOGICAL 1-SOLITON SOLUTION | Biswas-Milovic equation | Optical fibers | Schroedinger equation | Power law | Solitary waves | Mathematical analysis | Solitons | Nonlinearity | Mathematical models | Cases

Journal Article

Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 06/2016, Volume 127, Issue 12, pp. 4970 - 4983

This paper studies the exact solutions with parameters and optical soliton solutions of the (2 + 1)-dimensional hyperbolic nonlinear Schrödinger equation which...

Bright–dark-singular soliton solutions | Hyperbolic nonlinear Schrödinger equation | The soliton ansatz method | Modified simple equation method | Exp-function method | Bright-dark-singular soliton solutions | TRAVELING-WAVE SOLUTIONS | EVOLUTION | Hyperbolic nonlinear Schrodinger equation | OPTICS | TANH-FUNCTION METHOD | MEW | Mathematical analysis | Exact solutions | Solitons | Nonlinearity | Evolution | Schroedinger equation | Trigonometric functions | Solitary waves

Bright–dark-singular soliton solutions | Hyperbolic nonlinear Schrödinger equation | The soliton ansatz method | Modified simple equation method | Exp-function method | Bright-dark-singular soliton solutions | TRAVELING-WAVE SOLUTIONS | EVOLUTION | Hyperbolic nonlinear Schrodinger equation | OPTICS | TANH-FUNCTION METHOD | MEW | Mathematical analysis | Exact solutions | Solitons | Nonlinearity | Evolution | Schroedinger equation | Trigonometric functions | Solitary waves

Journal Article

Nonlinearity, ISSN 0951-7715, 01/2016, Volume 29, Issue 2, pp. 319 - 324

Two new integrable nonlocal Davey-Stewartson equations are introduced. These equations provide two-spatial dimensional analogues of the integrable, nonlocal...

integrable nonlocal Davey-Stewartson | nonlocal dbar | PT symmetry | MATHEMATICS, APPLIED | BI-HAMILTONIAN STRUCTURES | RECURSION OPERATORS | FOURIER-TRANSFORMS | PHYSICS, MATHEMATICAL | Construction | Mathematical analysis | Nonlinearity | Initial value problems | Schroedinger equation | Two dimensional | Nonlinear optics | Symmetry

integrable nonlocal Davey-Stewartson | nonlocal dbar | PT symmetry | MATHEMATICS, APPLIED | BI-HAMILTONIAN STRUCTURES | RECURSION OPERATORS | FOURIER-TRANSFORMS | PHYSICS, MATHEMATICAL | Construction | Mathematical analysis | Nonlinearity | Initial value problems | Schroedinger equation | Two dimensional | Nonlinear optics | Symmetry

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 07/2011, Volume 44, Issue 30, pp. 305203 - 22

The n-fold Darboux transformation (DT) is a 2 x 2 matrix for the Kaup-Newell (KN) system. In this paper, each element of this matrix is expressed by a ratio of...

WAVE | PHYSICS, MULTIDISCIPLINARY | INVERSE SCATTERING TRANSFORM | DNLS EQUATION | OPTICAL-WAVEGUIDES | PHYSICS, MATHEMATICAL | N-SOLITON SOLUTION | SELF-PHASE MODULATION | PULSES | Transformations (mathematics) | Mathematical analysis | Classification | Solitons | Determinants | Nonlinearity | Schroedinger equation | Derivatives

WAVE | PHYSICS, MULTIDISCIPLINARY | INVERSE SCATTERING TRANSFORM | DNLS EQUATION | OPTICAL-WAVEGUIDES | PHYSICS, MATHEMATICAL | N-SOLITON SOLUTION | SELF-PHASE MODULATION | PULSES | Transformations (mathematics) | Mathematical analysis | Classification | Solitons | Determinants | Nonlinearity | Schroedinger equation | Derivatives

Journal Article

1982, Mathematical notes, ISBN 9780691083186, Volume 29, 118

Book

Computer Physics Communications, ISSN 0010-4655, 01/2016, Volume 198, pp. 169 - 178

The classification of short hydrogen bonds depends on several factors including the shape and energy spacing between the nuclear eigenstates of the hydrogen....

2D Numerov method | DVR | Low barrier hydrogen bonds | Nuclear Schrödinger equation | Hydrogen bond classification | Short delocalized hydrogen bonds | 3D Numerov method | Chebyshev collocation | BARRIER HYDROGEN-BONDS | DELOCALIZATION | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PHOTOACTIVE YELLOW PROTEIN | Nuclear Schrodinger equation | Hydrogen | Nitriles | Algorithms | Bonds | Mathematical analysis | Solvers | Summaries | Mathematical models | Schroedinger equation | Two dimensional | Programming languages | Three dimensional

2D Numerov method | DVR | Low barrier hydrogen bonds | Nuclear Schrödinger equation | Hydrogen bond classification | Short delocalized hydrogen bonds | 3D Numerov method | Chebyshev collocation | BARRIER HYDROGEN-BONDS | DELOCALIZATION | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PHOTOACTIVE YELLOW PROTEIN | Nuclear Schrodinger equation | Hydrogen | Nitriles | Algorithms | Bonds | Mathematical analysis | Solvers | Summaries | Mathematical models | Schroedinger equation | Two dimensional | Programming languages | Three dimensional

Journal Article

Physics Letters A, ISSN 0375-9601, 03/2014, Volume 378, Issue 16-17, pp. 1113 - 1118

We study the -dimensional nonlinear Schrödinger equation with different forms of distributed transverse diffraction in anisotropic graded-index grating...

Controllable mechanism | Kuznetsov–Ma soliton | Nonlinear Schrödinger equation | Akhmediev breather | Kuznetsov-Ma soliton | PHYSICS, MULTIDISCIPLINARY | Nonlinear Schrodinger equation | MODEL | FIBER | MODULATION INSTABILITY | WAVE-GUIDES | MEDIA | OPTICS | INDEX | EXACT SPATIAL SIMILARITONS | SOLITON | Waveguides | Anisotropy | Forest management | Diffraction | Solitons | Solid state physics | Nonlinearity | Evolution | Schroedinger equation | Breathers

Controllable mechanism | Kuznetsov–Ma soliton | Nonlinear Schrödinger equation | Akhmediev breather | Kuznetsov-Ma soliton | PHYSICS, MULTIDISCIPLINARY | Nonlinear Schrodinger equation | MODEL | FIBER | MODULATION INSTABILITY | WAVE-GUIDES | MEDIA | OPTICS | INDEX | EXACT SPATIAL SIMILARITONS | SOLITON | Waveguides | Anisotropy | Forest management | Diffraction | Solitons | Solid state physics | Nonlinearity | Evolution | Schroedinger equation | Breathers

Journal Article