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Superlattices and microstructures, ISSN 0749-6036, 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
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
Journal Article
Nonlinear dynamics, ISSN 1573-269X, 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
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
Journal Article
Nonlinear dynamics, ISSN 1573-269X, 2015, 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
Journal Article
Physics letters. A, ISSN 0375-9601, 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
Journal Article
Physics Letters A, ISSN 0375-9601, 12/2017, Volume 381, Issue 48, pp. 3965 - 3971
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
Journal Article
Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, ISSN 1471-2946, 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
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 10/2016, Volume 86, Issue 2, pp. 877 - 889
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2017, Volume 262, Issue 1, pp. 506 - 558
Journal Article
Optik (Stuttgart), ISSN 0030-4026, 2017, Volume 140, pp. 136 - 144
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 09/2015, Volume 47, pp. 61 - 68
Journal Article
Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, ISSN 1471-2946, 2012, Volume 468, Issue 2142, pp. 1716 - 1740
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 02/2018, Volume 318, pp. 3 - 18
Journal Article