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 solutions to the model...

Chiral NLSE | Engineering | Vibration, Dynamical Systems, Control | Solitons and singular periodic solutions | Mechanics | Trial solution technique | Automotive Engineering | Mechanical Engineering | MECHANICS | ALFVEN WAVES | SOLITONS | APPROXIMATION | PERTURBATION | ENGINEERING, MECHANICAL | 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 | MECHANICS | ALFVEN WAVES | SOLITONS | APPROXIMATION | PERTURBATION | ENGINEERING, MECHANICAL | Solitary waves | Nonlinear equations | Schroedinger equation

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 345, Issue 1, pp. 90 - 108

In this paper we study the nonlinear Schrödinger–Maxwell equations { − Δ u + V ( x ) u + ϕ u = | u | p − 1 u in R 3 , − Δ ϕ = u 2 in R 3 . If V is a positive constant, we prove the existence of a ground state solution...

Nonlinear Schrödinger–Maxwell equations | Ground state solutions | Nonlinear Schrödinger-Maxwell equations | SYSTEM | EXISTENCE | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | SCALAR FIELD-EQUATIONS | NONEXISTENCE | nonlinear schrodinger-maxwell equations | COMPETING POTENTIAL FUNCTIONS | POSITIVE SOLUTIONS | CALCULUS | ground state solutions | CONCENTRATION-COMPACTNESS PRINCIPLE | MATHEMATICS | MULTIPLE SOLITARY WAVES

Nonlinear Schrödinger–Maxwell equations | Ground state solutions | Nonlinear Schrödinger-Maxwell equations | SYSTEM | EXISTENCE | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | SCALAR FIELD-EQUATIONS | NONEXISTENCE | nonlinear schrodinger-maxwell equations | COMPETING POTENTIAL FUNCTIONS | POSITIVE SOLUTIONS | CALCULUS | ground state solutions | CONCENTRATION-COMPACTNESS PRINCIPLE | MATHEMATICS | MULTIPLE SOLITARY WAVES

Journal Article

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Dynamics of the optical solitons for a (2+1)-dimensional nonlinear Schrödinger equation

Superlattices and Microstructures, ISSN 0749-6036, 01/2017, Volume 101, pp. 522 - 528

In this paper, a nonlinear Schrödinger equation (NLS) has been studied, which can describe the propagation and interaction of optical solitons in a material with x-directional localized and y-directional nonlocal non-linearities...

Optical solitons | Hermite-Gaussian vortex solitons | Nonlinear Schrödinger equation | PHYSICS, CONDENSED MATTER | Nonlinear Schrodinger equation

Optical solitons | Hermite-Gaussian vortex solitons | Nonlinear Schrödinger equation | PHYSICS, CONDENSED MATTER | Nonlinear Schrodinger equation

Journal Article

Optik, ISSN 0030-4026, 09/2017, Volume 145, pp. 79 - 88

In optical fibers, the higher order nonlinear Schrödinger equations describe propagation of ultra-short pluse...

Nonlinear higher order Schrödinger equations | Positive non-integers balance numbers | Solitary wave solutions | Modified simple equation method | Solitons | TANH METHOD | Nonlinear higher order Schrodinger equations | 1-SOLITON SOLUTION | TRAVELING-WAVE SOLUTIONS | STABILITY ANALYSIS | HIGHER-ORDER | OPTICS | KDV | BRIGHT

Nonlinear higher order Schrödinger equations | Positive non-integers balance numbers | Solitary wave solutions | Modified simple equation method | Solitons | TANH METHOD | Nonlinear higher order Schrodinger equations | 1-SOLITON SOLUTION | TRAVELING-WAVE SOLUTIONS | STABILITY ANALYSIS | HIGHER-ORDER | OPTICS | KDV | BRIGHT

Journal Article

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

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

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

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

A (3 + 1)-dimensional partially nonlocal nonlinear Schrödinger equation is considered, and approximate spatiotemporal Hermite...

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

Physics Letters A, ISSN 0375-9601, 04/2019, Volume 383, Issue 12, pp. 1274 - 1282

... Schrödinger equation with damping and parametric drive. Here, we justify the approximation by looking for the error bound with the method of energy estimates...

Discrete nonlinear Schrödinger equation | Discrete Klein–Gordon equation | Discrete breather | Discrete soliton | Small-amplitude approximation | WAVES | PHYSICS, MULTIDISCIPLINARY | Discrete Klein-Gordon equation | DOMAIN-WALLS | BREATHERS | LATTICES | Discrete nonlinear Schrodinger equation | Islamic schools | Analysis | Numerical analysis

Discrete nonlinear Schrödinger equation | Discrete Klein–Gordon equation | Discrete breather | Discrete soliton | Small-amplitude approximation | WAVES | PHYSICS, MULTIDISCIPLINARY | Discrete Klein-Gordon equation | DOMAIN-WALLS | BREATHERS | LATTICES | Discrete nonlinear Schrodinger equation | Islamic schools | Analysis | Numerical analysis

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Asymptotic expansions and solitons of the Camassa–Holm – nonlinear Schrödinger equation

Physics Letters A, ISSN 0375-9601, 12/2017, Volume 381, Issue 48, pp. 3965 - 3971

We study a deformation of the defocusing nonlinear Schrödinger (NLS) equation, the defocusing Camassa...

Camassa–Holm NLS | Multiscale expansion | Dark solitons | Antidark solitons | PHYSICS, MULTIDISCIPLINARY | INVERSE SCATTERING TRANSFORM | AMPLITUDE | INSTABILITIES | SOLITARY WAVES | SYSTEMS | MEDIA | DARK OPTICAL SOLITONS | KORTEWEG-DE-VRIES | Camassa Holm NLS | Mechanical engineering | Analysis | Numerical analysis

Camassa–Holm NLS | Multiscale expansion | Dark solitons | Antidark solitons | PHYSICS, MULTIDISCIPLINARY | INVERSE SCATTERING TRANSFORM | AMPLITUDE | INSTABILITIES | SOLITARY WAVES | SYSTEMS | MEDIA | DARK OPTICAL SOLITONS | KORTEWEG-DE-VRIES | Camassa Holm NLS | Mechanical engineering | Analysis | Numerical analysis

Journal Article

Physics Letters A, ISSN 0375-9601, 08/2017, Volume 381, Issue 30, pp. 2380 - 2385

In this paper, we succeed to bilinearize the PT-invariant nonlocal nonlinear Schrödinger (NNLS) equation through a nonstandard procedure and present more general bright soliton solutions...

Bright soliton solution | [formula omitted]-symmetry | Nonstandard bilinearization | Nonlocal nonlinear Schrödinger equation | PT-symmetry | Nonlocal nonlinear Schrodinger equation | 2T-symmetry | PHYSICS, MULTIDISCIPLINARY

Bright soliton solution | [formula omitted]-symmetry | Nonstandard bilinearization | Nonlocal nonlinear Schrödinger equation | PT-symmetry | Nonlocal nonlinear Schrodinger equation | 2T-symmetry | PHYSICS, MULTIDISCIPLINARY

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The mixed coupled nonlinear Schrödinger equation on the half-line via the Fokas method

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 11/2016, Volume 472, Issue 2195, p. 20160588

In this paper, we implement the Fokas method to study initial-boundary value problems of the mixed coupled nonlinear Schrdinger equation formulated on the half-line with Lax pairs involving 3 x 3 matrices...

Mixed coupled nonlinear Schrödinger equation | Riemann-Hilbert problem | Initial-boundary value problem | mixed coupled nonlinear Schrodinger equation | MULTIDISCIPLINARY SCIENCES | BOUNDARY-VALUE-PROBLEMS | ASYMPTOTICS | EVOLUTION-EQUATIONS | initial-boundary value problem | 1008 | mixed coupled nonlinear Schrödinger equation | 120 | Riemann–Hilbert problem

Mixed coupled nonlinear Schrödinger equation | Riemann-Hilbert problem | Initial-boundary value problem | mixed coupled nonlinear Schrodinger equation | MULTIDISCIPLINARY SCIENCES | BOUNDARY-VALUE-PROBLEMS | ASYMPTOTICS | EVOLUTION-EQUATIONS | initial-boundary value problem | 1008 | mixed coupled nonlinear Schrödinger equation | 120 | Riemann–Hilbert problem

Journal Article

Optik, ISSN 0030-4026, 05/2016, Volume 127, Issue 10, pp. 4222 - 4245

We analytically study the Schrödinger type nonlinear evolution equations by improved tan(Φ(ξ)/2)-expansion method...

Trigonometric function solution | Hyperbolic function solution | Improved tan(Φ(ξ)/2)-expansion method | Schrödinger equation | Exponential solution and rational solution | Improved tan(Pdbl(ξ)/2)-expansion method | TRAVELING-WAVE SOLUTIONS | Improved tan(Phi(xi)/2)-expansion method | Schrodinger equation | PARTIAL-DIFFERENTIAL-EQUATIONS | OPTICS | Searching | Mathematical analysis | Nonlinear differential equations | Solitons | Nonlinear evolution equations | Mathematical models | Schroedinger equation | Hyperbolic functions

Trigonometric function solution | Hyperbolic function solution | Improved tan(Φ(ξ)/2)-expansion method | Schrödinger equation | Exponential solution and rational solution | Improved tan(Pdbl(ξ)/2)-expansion method | TRAVELING-WAVE SOLUTIONS | Improved tan(Phi(xi)/2)-expansion method | Schrodinger equation | PARTIAL-DIFFERENTIAL-EQUATIONS | OPTICS | Searching | Mathematical analysis | Nonlinear differential equations | Solitons | Nonlinear evolution equations | Mathematical models | Schroedinger equation | Hyperbolic functions

Journal Article

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Rogue wave solutions of the (2+1)-dimensional derivative nonlinear Schrödinger equation

Nonlinear Dynamics, ISSN 0924-090X, 10/2016, Volume 86, Issue 2, pp. 877 - 889

In this paper, we focus on the construction of rogue wave solutions for the (2+1)-dimensional derivative nonlinear Schrodinger equation...

(2+1)-dimensional derivative nonlinear Schrödinger equation | Generalized Darboux transformation | Rogue wave | DARBOUX TRANSFORMATION | MECHANICS | (2+1)-dimensional derivative nonlinear Schrodinger equation | MECHANISMS | OPTICS | ENGINEERING, MECHANICAL | SOLITON | Water waves | Plane waves | Anti takeover strategy | Transformations | Schroedinger equation | Memorial services | C plus plus | Nonlinear dynamics | Determinants | Nonlinearity | Derivatives

(2+1)-dimensional derivative nonlinear Schrödinger equation | Generalized Darboux transformation | Rogue wave | DARBOUX TRANSFORMATION | MECHANICS | (2+1)-dimensional derivative nonlinear Schrodinger equation | MECHANISMS | OPTICS | ENGINEERING, MECHANICAL | SOLITON | Water waves | Plane waves | Anti takeover strategy | Transformations | Schroedinger equation | Memorial services | C plus plus | Nonlinear dynamics | Determinants | Nonlinearity | Derivatives

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 01/2017, Volume 262, Issue 1, pp. 506 - 558

... Schrödinger equation formulated on the finite interval with 3×3 Lax pairs. The solution can be written in terms of the solution of a 3×3 Riemann–Hilbert problem...

Integrable system | Initial–boundary value problem | Dirichlet-to-Neumann map | Riemann–Hilbert problem | Coupled nonlinear Schrödinger equation | MATHEMATICS | Riemann-Hilbert problem | Coupled nonlinear Schrodinger equation | INTEGRABILITY | UNIFIED TRANSFORM METHOD | LONG-TIME ASYMPTOTICS | Initial-boundary value problem | EVOLUTION-EQUATIONS | Analysis | Methods | Differential equations

Integrable system | Initial–boundary value problem | Dirichlet-to-Neumann map | Riemann–Hilbert problem | Coupled nonlinear Schrödinger equation | MATHEMATICS | Riemann-Hilbert problem | Coupled nonlinear Schrodinger equation | INTEGRABILITY | UNIFIED TRANSFORM METHOD | LONG-TIME ASYMPTOTICS | Initial-boundary value problem | EVOLUTION-EQUATIONS | Analysis | Methods | Differential equations

Journal Article

Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 07/2017, Volume 140, pp. 136 - 144

•Unstable nonlinear Schrödinger equation is considered.•Extended simple equation method is discussed...

Solitary wave solutions | Simple equation method | Unstable nonlinear Schrödinger equation | Solitons | Modify unstable nonlinear Schrödinger equation | SOLITON-SOLUTIONS | equation | Modify unstable nonlinear Schrodinger | Unstable nonlinear Schrodinger equation | OPTICS

Solitary wave solutions | Simple equation method | Unstable nonlinear Schrödinger equation | Solitons | Modify unstable nonlinear Schrödinger equation | SOLITON-SOLUTIONS | equation | Modify unstable nonlinear Schrodinger | Unstable nonlinear Schrodinger equation | OPTICS

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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...

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

Applied Mathematics Letters, ISSN 0893-9659, 09/2015, Volume 47, pp. 61 - 68

... Schrödinger equations. The two-parameter (ϵx,ϵt) family also brings insight into a one-to-one connection between four points (ϵx,ϵt) (or complex numbers ϵx+iϵt) with {I,P,T,PT...

Conservation laws | [formula omitted] symmetry | Two-parameter family of nonlocal vector nonlinear Schrödinger equations | Lax pair | Solitons | equations | Two-parameter family of nonlocal | vector nonlinear Schrödinger | PT symmetry | MATHEMATICS, APPLIED | Two-parameter family of nonlocal vector nonlinear Schrodinger equations | POTENTIALS | PHOTONIC LATTICES | ROGUE WAVES | PARITY-TIME SYMMETRY | DYNAMICS | REAL | OPTICS | NON-HERMITIAN HAMILTONIANS

Conservation laws | [formula omitted] symmetry | Two-parameter family of nonlocal vector nonlinear Schrödinger equations | Lax pair | Solitons | equations | Two-parameter family of nonlocal | vector nonlinear Schrödinger | PT symmetry | MATHEMATICS, APPLIED | Two-parameter family of nonlocal vector nonlinear Schrodinger equations | POTENTIALS | PHOTONIC LATTICES | ROGUE WAVES | PARITY-TIME SYMMETRY | DYNAMICS | REAL | OPTICS | NON-HERMITIAN HAMILTONIANS

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 02/2018, Volume 318, pp. 3 - 18

...–Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). We shall use HBVMs for solving the nonlinear Schrödinger equation (NLSE...

Nonlinear Schrödinger equation | Hamiltonian partial differential equations | Energy-conserving methods | Line integral methods | Hamiltonian Boundary Value methods | HBVMs | CONSERVATION ISSUES | MATHEMATICS, APPLIED | SYMPLECTIC METHODS | Nonlinear Schrodinger equation | STEP METHODS | IMPLEMENTATION | IMPLICIT METHODS | FAMILY | NUMERICAL-SOLUTION | GAUSS COLLOCATION | INTEGRATORS | Usage | Methods | Differential equations

Nonlinear Schrödinger equation | Hamiltonian partial differential equations | Energy-conserving methods | Line integral methods | Hamiltonian Boundary Value methods | HBVMs | CONSERVATION ISSUES | MATHEMATICS, APPLIED | SYMPLECTIC METHODS | Nonlinear Schrodinger equation | STEP METHODS | IMPLEMENTATION | IMPLICIT METHODS | FAMILY | NUMERICAL-SOLUTION | GAUSS COLLOCATION | INTEGRATORS | Usage | Methods | Differential equations

Journal Article

Scientific Reports, ISSN 2045-2322, 03/2016, Volume 6, Issue 1, p. 23478

.... The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrodinger (NLS...

MULTIDISCIPLINARY SCIENCES | REAL SPECTRA | LATTICES | HAMILTONIANS | OPTICAL SOLITONS | FINANCIAL ROGUE WAVES | GUIDES | Adiabatic | Optics | Nonlinear equations | Mathematical models

MULTIDISCIPLINARY SCIENCES | REAL SPECTRA | LATTICES | HAMILTONIANS | OPTICAL SOLITONS | FINANCIAL ROGUE WAVES | GUIDES | Adiabatic | Optics | Nonlinear equations | Mathematical models

Journal Article