Nonlinear dynamics, ISSN 1573-269X, 12/2015, Volume 84, Issue 3, pp. 1157 - 1161

A (3 + 1)-dimensional partially nonlocal nonlinear Schrodinger equation is considered, and approximate spatiotemporal Hermite-Gaussian soliton solutions are obtained using the Hirota method...

Spatiotemporal Hermiteâ€“Gaussian solitons | Nonlinear SchrÃ¶dinger equation | Partially nonlocal nonlinearity | Mechanics | Engineering | Technology | Engineering, Mechanical | Science & Technology | Gaussian processes | Solitary waves | Schroedinger equation | Nonlinear dynamics | Nonlinearity | Approximation | Solitons

Spatiotemporal Hermiteâ€“Gaussian solitons | Nonlinear SchrÃ¶dinger equation | Partially nonlocal nonlinearity | Mechanics | Engineering | Technology | Engineering, Mechanical | Science & Technology | Gaussian processes | Solitary waves | Schroedinger equation | Nonlinear dynamics | Nonlinearity | Approximation | Solitons

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 SchrÃ¶dinger equation governing the evolution of slowly modulated plane-wave solutions to the nonlinear Klein...

Engineering | Vibration, Dynamical Systems, Control | Nonlinear Kleinâ€“Gordon equation | Method of multiple scales | Nonlinear dispersion | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Nonlinear SchrÃ¶dinger equation | Envelope | Multiple-scale analysis | Mechanics | Technology | Engineering, Mechanical | Science & Technology | Nonlinearity | Schroedinger equation | Polynomials | Klein-Gordon equation | Wave packets

Engineering | Vibration, Dynamical Systems, Control | Nonlinear Kleinâ€“Gordon equation | Method of multiple scales | Nonlinear dispersion | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Nonlinear SchrÃ¶dinger equation | Envelope | Multiple-scale analysis | Mechanics | Technology | Engineering, Mechanical | Science & Technology | Nonlinearity | Schroedinger equation | Polynomials | Klein-Gordon equation | Wave packets

Journal Article

Nonlinear dynamics, ISSN 1573-269X, 03/2016, Volume 85, Issue 2, pp. 813 - 816

This paper applied the trial solution technique to chiral nonlinear Schrodingerâ€™s equation in (1
$$+$$
+
2)-dimensions. This led to solitons and other solutions to the model...

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

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

.... We show that, while in the former case the Schrodinger equation stays linear, in the latter case one ends up with the so-called Schrodinger-Newton equation, which involves a nonlinear, non-local...

semi-classical gravity | collapse of the wave-function | SchrÃ¶dinger-Newton equation | Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | Gravitational fields | Signaling | Gravitation | Schroedinger equation | Quantum gravity | Gravitational collapse | Collapse | Mathematical analysis | Nonlinearity | Mathematical models | Signalling

semi-classical gravity | collapse of the wave-function | SchrÃ¶dinger-Newton equation | Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | Gravitational fields | Signaling | Gravitation | Schroedinger equation | Quantum gravity | Gravitational collapse | Collapse | Mathematical analysis | Nonlinearity | Mathematical models | Signalling

Journal Article

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

... SchrÃ¶dinger equation with linear and parabolic potentials and a standard nonlinear SchrÃ¶dinger equation is given, and an exact superposed Akhmediev breather solution in certain parameter conditions is obtained...

Superposed Akhmediev breather | Controllable dynamical behaviors | Nonlinear SchrÃ¶dinger equation | Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | 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 SchrÃ¶dinger equation | Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | 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

International journal of modern physics. A, Particles and fields, gravitation, cosmology, ISSN 1793-656X, 06/2019, Volume 34, Issue 15, p. 1950074

In this paper, we discuss the relation between the [Formula: see text]D nonlinear SchrÃ¶dinger equation and the KdV equation...

Physical Sciences | Physics, Nuclear | Physics, Particles & Fields | Physics | Science & Technology

Physical Sciences | Physics, Nuclear | Physics, Particles & Fields | Physics | Science & Technology

Journal Article

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

.... As we know, the super-integrable soliton equation hierarchies with four potentials are discussed...

Super-Dirac equation | Engineering | Vibration, Dynamical Systems, Control | Super-SchrÃ¶dinger equation | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Darboux transformation | Exact solution | Mechanics | Technology | Engineering, Mechanical | Science & Technology | Inhomogeneous media | Transformations | Schroedinger equation | Hierarchies | Solitary waves | Dirac equation

Super-Dirac equation | Engineering | Vibration, Dynamical Systems, Control | Super-SchrÃ¶dinger equation | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Darboux transformation | Exact solution | Mechanics | Technology | Engineering, Mechanical | Science & Technology | 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...

Science & Technology - Other Topics | Multidisciplinary Sciences | Science & Technology | Models, Theoretical | Nonlinear Dynamics | Singularities | Partial differential equations | Solitons | Optics | Waves | Optical waveguides | Information science | Mathematical analysis | Klein-Gordon equation | Schroedinger equation | Mathematical models | Solitary waves | Symmetry | Breathers

Science & Technology - Other Topics | Multidisciplinary Sciences | Science & Technology | Models, Theoretical | Nonlinear Dynamics | Singularities | Partial differential equations | Solitons | Optics | Waves | Optical waveguides | Information science | Mathematical analysis | Klein-Gordon equation | Schroedinger equation | Mathematical models | Solitary waves | Symmetry | Breathers

Journal Article

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

The Wheelerâ€“DeWitt equation was proposed 50 years ago and until now it is the cornerstone of most approaches to quantization of gravity...

extended phase space | quantum gravity | The Wheeler-DeWitt equation

extended phase space | quantum gravity | The Wheeler-DeWitt equation

Journal Article

Nonlinearity, ISSN 1361-6544, 02/2016, 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 | Physical Sciences | Mathematics | Mathematics, Applied | Physics | Physics, Mathematical | Science & Technology | Construction | Mathematical analysis | Nonlinearity | Initial value problems | Schroedinger equation | Two dimensional | Nonlinear optics | Symmetry

integrable nonlocal Davey-Stewartson | nonlocal dbar | PT symmetry | Physical Sciences | Mathematics | Mathematics, Applied | Physics | Physics, Mathematical | Science & Technology | Construction | Mathematical analysis | Nonlinearity | Initial value problems | Schroedinger equation | Two dimensional | Nonlinear optics | Symmetry

Journal Article

Mathematical models & methods in applied sciences, ISSN 0218-2025, 07/2015, Volume 25, Issue 8, pp. 1447 - 1476

We investigate a class of nonlinear Schrodinger equations with a generalized Choquard nonlinearity and fractional diffusion...

existence | multiplicity | nonexistence | Fractional Laplacian | Choquard equation | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

existence | multiplicity | nonexistence | Fractional Laplacian | Choquard equation | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

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

High-order rogue wave solutions of the Benjaminâ€“Ono equation and the nonlocal nonlinear...

Bilinear method | Rogue waves | Benjamin-Ono equation | Nonlocal nonlinear SchrÃ¶dinger equation | Physics, Condensed Matter | Physical Sciences | Physics | Physics, Mathematical | Science & Technology | Physics, Applied

Bilinear method | Rogue waves | Benjamin-Ono equation | Nonlocal nonlinear SchrÃ¶dinger equation | Physics, Condensed Matter | Physical Sciences | Physics | Physics, Mathematical | Science & Technology | Physics, Applied

Journal Article

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

... equation are given explicitly by different seed solutions. In particular, the rogue wave and rational traveling solution are two kinds of new solutions...

Physics, Multidisciplinary | Physical Sciences | Physics | Physics, Mathematical | Science & Technology | Transformations (mathematics) | Mathematical analysis | Classification | Solitons | Determinants | Nonlinearity | Schroedinger equation | Derivatives

Physics, Multidisciplinary | Physical Sciences | Physics | Physics, Mathematical | Science & Technology | Transformations (mathematics) | Mathematical analysis | Classification | Solitons | Determinants | Nonlinearity | Schroedinger equation | Derivatives

Journal Article