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Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 05/2009, Volume 14, Issue 5, pp. 2034 - 2045
Journal Article
Journal of Modern Optics, ISSN 0950-0340, 07/2018, Volume 65, Issue 12, pp. 1431 - 1436
 A wide range of problems in different fields of the applied sciences especially non-linear optics is described by non-linear Schrödinger's equations (NLSEs).... 
optical soliton solutions | generalized Kudryashov method | anti-cubic term | Cubic-quintic non-linear Schrödinger's equation | GORDON EQUATIONS | TRAVELING-WAVE SOLUTIONS | Cubic-quintic non-linear Schrodinger's equation | RATIONAL-FUNCTION METHOD | OPTICS | TANH-FUNCTION METHOD | Optics | Nonlinear optics | Nonlinear equations
Journal Article
European Journal of Applied Mathematics, ISSN 0956-7925, 10/2016, Volume 27, Issue 5, pp. 726 - 737
The discrete non-linear Schrödinger equation is one of the most important inherently discrete models, having a crucial role in the modelling of a great variety... 
Key words: existence | discrete non-linear Schrödinger equations | critical point theory | solitons | Nonlinear equations | Mathematical models | Schrodinger equation | Approximation | Mathematical analysis | Solitons | Condensing | Nonlinearity | Schroedinger equation | Biology
Journal Article
Izvestiya Mathematics, ISSN 1064-5632, 2015, Volume 79, Issue 2, pp. 346 - 374
We study the large-time behaviour of solutions of the Cauchy problem for a non-linear Schrodinger equation. We consider the interaction between the resonance... 
Schrödinger equation | Cubic non-linearity | Large-time asymptotics | MATHEMATICS | Schrodinger equation | ONE SPACE DIMENSION | GLOBAL EXISTENCE | large-time asymptotics | ASYMPTOTICS | cubic non-linearity | SCATTERING | Decay rate | Asymptotic properties | Mathematical analysis | Dissipation | Nonlinearity | Schroedinger equation | Representations | Cauchy problem
Journal Article
Journal of the Australian Mathematical Society, ISSN 1446-7887, 02/2015, Volume 98, Issue 1, pp. 104 - 116
We consider the semilinear Schrodinger equation {-Delta u + V(x)u = f(x, u), x is an element of R-N, u is an element of H-1 (R-N), where f (x, u) is... 
non-Nehari-manifold method | Schrodinger equation | ground state solutions of Nehari-Pankov type | asymptotically linear | MATHEMATICS | SUPER | PART
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 12/2006, Volume 166, Issue 3, pp. 645 - 675
We prove, for the energy critical, focusing NLS, that for data whose energy is smaller than that of the standing wave, and whose homogeneous Sobolev norm H^1... 
Mathematics, general | Mathematics | EXISTENCE | MATHEMATICS | NON-LINEAR SCHRODINGER | MASS | CAUCHY-PROBLEM | CRITICAL POWER | TIME | COMPACTNESS | KLEIN-GORDON EQUATIONS | Mathematics - Analysis of PDEs
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 09/2013, Volume 18, Issue 9, pp. 2420 - 2425
► Exact bright and dark solitary wave solution of the nonlinear Schrodinger equation in non-Kerr medium is reported. ► Solitary wave parameters along with the... 
Pulse propagation | Modulation Instability | Optical solitons | Non linear Schrodinger equation | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | DARK SOLITON | PULSES | TRANSMISSION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYMBOLIC COMPUTATION | OPTICAL-FIBERS | PHYSICS
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 2019, Volume 52, Issue 3, p. 35202
We investigate dispersive and Strichartz estimates for the Schrodinger time evolution propagator e(-itH) on a star-shaped metric graph. The linear operator, H,... 
Schrodinger operator | quantum graphs | Strichartz estimates | non- linear Schrodinger equation | dispersion | LAPLACIANS | NETWORK | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | QUANTUM GRAPH | THIN FIBERS
Journal Article
IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), ISSN 0272-4960, 2017, Volume 82, Issue 1, pp. 131 - 151
The inverse scattering transform for the focusing non-linear Schrodinger (NLS) equation with non-zero boundary conditions at infinity and double zeros of the... 
Inverse scattering | Non-linear schrodinger equation | Non-zero boundary conditions | Solitons | MATHEMATICS, APPLIED | non-zero boundary conditions | WAVES | non-linear Schrodinger equation | inverse scattering | MODULATION
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 05/2009, Volume 14, Issue 5, pp. 1993 - 1998
This paper studies the nonlinear Schrödinger's equation in a non-Kerr law media. The travelling wave ansatz is used to carry out the analysis. The doubly... 
Nonlinear Schrödinger's equation | Travelling wave | Non-Kerr law nonlinearity | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SOLITONS | PHYSICS, FLUIDS & PLASMAS | Nonlinear Schrodinger's equation | PHYSICS, MATHEMATICAL
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2018, Volume 459, Issue 2, pp. 932 - 944
We consider an inverse scattering problem for a non-linear Schrödinger equation with a non-linearity of power-type. Applying the time-dependent technique,... 
Inverse scattering problems | Non-linear Schrödinger equations | Scattering theory | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | KLEIN-GORDON EQUATION | RECONSTRUCTION | HALF-LINE | Non-linear Schrodinger equations
Journal Article
Studies in Applied Mathematics, ISSN 0022-2526, 2018
We study the defocusing Non-Linear Schrödinger (NLS) equation written in hydrodynamic form through the Madelung transform. From the mathematical point of view,... 
Quantum Physics | Mathematics | Mathematical Physics | Analysis of PDEs | Physics
Journal Article
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, ISSN 1534-0392, 03/2012, Volume 11, Issue 2, pp. 587 - 626
The equation -epsilon(2)Delta u + F(V(x), u) = 0 is considered in R-n. It is assumed that V possesses a set of critical points B for which the values of V and... 
EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | multibumps | BOUND-STATES | PARTIAL-DIFFERENTIAL-EQUATIONS | THEOREM | Non-linear Schrodinger equation
Journal Article
Applicable Analysis, ISSN 0003-6811, 09/2010, Volume 89, Issue 9, pp. 1541 - 1557
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 2010, Volume 23, Issue 7, pp. 751 - 755
A model for the evolution of envelope waves in non-linear dispersive media is analyzed. With the help of coupled Non-Linear Schrödinger Equations (NLSE), the... 
Modulation instability | Coupled non-linear Schrödinger equations | Coupled Non-Linear Schrödinger Equations | Modulation Instability | MATHEMATICS, APPLIED | WAVES | SOLITONS | Coupled non-linear Schrodinger equations | MODULATIONAL INSTABILITY | MEDIA
Journal Article
Nonlinearity, ISSN 0951-7715, 07/2017, Volume 30, Issue 8, pp. 3271 - 3303
We consider a nonlinear Schrodinger equation (NLS) posed on a graph (or network) composed of a generic compact part to which a finite number of half-lines are... 
non-linear Schrodinger equation | concentrationcompactness techniques | quantum graphs | MATHEMATICS, APPLIED | TADPOLE GRAPH | STANDING WAVES | concentration-compactness techniques | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | CONSTRAINED ENERGY MINIMIZATION
Journal Article
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