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Journal of Differential Equations, ISSN 0022-0396, 09/2019, Volume 267, Issue 6, pp. 3646 - 3692
The current paper is a continuation of our early work . We use the techniques and properties of -modulation spaces developed in to study the Cauchy problem for... 
Derivative NLS | α-Modulation space | Global well-posedness | Ill-posedness
Journal Article
Journal of Hyperbolic Differential Equations, ISSN 0219-8916, 09/2017, Volume 14, Issue 3, pp. 455 - 485
We consider the Cauchy problem for the cubic focusing nonlinear Schrodinger (NLS) equation on the line with initial datum close to an N-soliton. Using the... 
Cubic nonlinear Schrödinger equation | inverse scattering | Riemann-Hilbert problem | method | asymptotic stability | solitons | MATHEMATICS, APPLIED | Cubic nonlinear Schrodinger equation | (partial derivative)over-bar-method | PHYSICS, MATHEMATICAL | Mathematics - Analysis of PDEs
Journal Article
Dynamics of Partial Differential Equations, ISSN 1548-159X, 2017, Volume 14, Issue 3, pp. 271 - 294
We prove the global existence result for the derivative NLS equation in the case when the initial datum includes a finite number of solitons. This is achieved... 
Global existence | Inverse scattering transform | Derivative nonlinear Schrödinger equation | Bäcklund transformation | Solitons | MATHEMATICS, APPLIED | INVERSE SCATTERING | SOLITARY WAVES | STABILITY | WELL-POSEDNESS | Backlund transformation | NONLINEAR SCHRODINGER-EQUATION | Derivative nonlinear Schrodinger equation
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 03/2020, Volume 192, p. 111665
We study the stability theory of solitary wave solutions for a type of derivative nonlinear Schrödinger equation The equation has a two-parameter family of... 
Derivative NLS | Orbital instability | Solitary wave solutions | Degenerate case
Journal Article
Open Cybernetics and Systemics Journal, ISSN 1874-110X, 2015, Volume 9, Issue 1, pp. 1567 - 1575
Journal Article
Journal Article
Journal of Electromagnetic Waves and Applications, ISSN 0920-5071, 09/2017, Volume 31, Issue 14, pp. 1353 - 1362
The generalized derivative higher order non-linear Schrödinger (DNLS) equation describes pluses propagation in optical fibers and can be regarded as a special... 
solitary wave solutions | mathematical physics methods | Generalized higher order derivative NLS equation | PHYSICS, APPLIED | ZAKHAROV-KUZNETSOV EQUATION | WAVE SOLUTIONS | BACKLUND TRANSFORMATION | ROGUE WAVES | ENGINEERING, ELECTRICAL & ELECTRONIC
Journal Article
Wave Motion, ISSN 0165-2125, 06/2017, Volume 71, pp. 93 - 100
Binary waveguide arrays are linear arrays of optical waveguides with binary alternation of parameters, and have been of recent interest. They can be modeled by... 
Discrete NLS | Optical lattices | Lattice wave equations | Binary waveguide arrays | Long wave approximation | Third derivative NLS | ACOUSTICS | MECHANICS | SOLITONS | INTEGRATION | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | Waveguides
Journal Article
Studies in Applied Mathematics, ISSN 0022-2526, 05/2013, Volume 130, Issue 4, pp. 317 - 344
By means of certain limit technique, two kinds of generalized Darboux transformations are constructed for the derivative nonlinear Schrödinger equations... 
MATHEMATICS, APPLIED | MULTISOLITON SOLUTIONS | NLS EQUATION | SOLITONS | ROGUE WAVES | Construction | Mathematical analysis | Determinants | Nonlinearity | Transformations | Schroedinger equation | Derivatives
Journal Article
Discrete and Continuous Dynamical Systems - Series B, ISSN 1531-3492, 08/2016, Volume 21, Issue 6, pp. 1813 - 1837
Systems of ODE's with forms related to the discrete nonlinear Schrodinger equation arise in a variety of semi-classical molecular models, such as models of... 
Discrete NLS | Optical lattices | Binary waveguide arrays | Long wave approximation | Lattice wave equations | Airy PDE | Third derivative NLS | lattice wave equations | long wave approximation | MATHEMATICS, APPLIED | third derivative NLS | SOLITONS | INTEGRATION | optical lattices | discrete NLS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 02/2017, Volume 262, Issue 3, pp. 1671 - 1689
We study the stability theory of solitary wave solutions for a type of the derivative nonlinear Schrödinger equation The equation has a two-parameter family of... 
Derivative NLS | Orbital instability | Solitary wave solutions | MATHEMATICS | INITIAL-VALUE PROBLEM | STABILITY | ENERGY SPACE | GLOBAL WELL-POSEDNESS
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 03/2019, Volume 88, Issue 316, pp. 717 - 749
Journal Article
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 11/2018, Volume 35, Issue 7, pp. 1947 - 1973
We study the initial-boundary value problem for the derivative nonlinear Schrödinger (DNLS) equation. More precisely we study the wellposedness theory and the... 
Derivative NLS | Initial-boundary value problems | Nonlinear smoothing | Wellposedness theory | MATHEMATICS, APPLIED | KORTEWEG-DE-VRIES | REGULARITY PROPERTIES | GLOBAL WELL-POSEDNESS | ZAKHAROV SYSTEM
Journal Article
Communications in Theoretical Physics, ISSN 0253-6102, 12/2015, Volume 64, Issue 6, pp. 605 - 618
Fokas system is the simplest (2+1)-dimensional extension of the nonlinear Schrodinger equation (Eq. (2), Inverse Problems 10 (1994) L19-L22). By using the... 
rogue wave | rational solution | Fokas system | bilinear transformation method | KP-I EQUATION | NLS EQUATION | ROGUE WAVE SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | DYNAMICS | NONLINEAR SCHRODINGER-EQUATION | Inverse problems | Wave propagation | Preserves | Determinants | Constants | Transformations | Schroedinger equation | Derivatives
Journal Article