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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
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
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
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
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
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 05/2016, Volume 71, Issue 10, pp. 2001 - 2007
Journal Article
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
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
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 07/2018, Volume 93, Issue 2, pp. 721 - 731
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
Journal Article
Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 06/2016, Volume 127, Issue 12, pp. 4970 - 4983
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
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
Journal Article
Physics Letters A, ISSN 0375-9601, 03/2014, Volume 378, Issue 16-17, pp. 1113 - 1118
Journal Article