Nonlinear Dynamics, ISSN 0924-090X, 1/2012, Volume 67, Issue 1, pp. 619 - 627

In this paper, we are concerned with the problem of applying cubic non-polynomial spline functions to develop a numerical method for obtaining approximation...

Engineering | Vibration, Dynamical Systems, Control | Non-polynomial spline | Mechanics | Automotive Engineering | Von Neumann stability | Mechanical Engineering | Non-linear Schrodinger equation | BOUNDARY-VALUE-PROBLEMS | MECHANICS | ENGINEERING, MECHANICAL | Analysis | Universities and colleges | Nonlinear equations | Numerical analysis | Schrodinger equation | Error analysis | Mathematical analysis | Numerical methods | Spline functions | Truncation errors | Schroedinger equation | Polynomials | Linearization | Approximation | Nonlinearity | Mathematical models

Engineering | Vibration, Dynamical Systems, Control | Non-polynomial spline | Mechanics | Automotive Engineering | Von Neumann stability | Mechanical Engineering | Non-linear Schrodinger equation | BOUNDARY-VALUE-PROBLEMS | MECHANICS | ENGINEERING, MECHANICAL | Analysis | Universities and colleges | Nonlinear equations | Numerical analysis | Schrodinger equation | Error analysis | Mathematical analysis | Numerical methods | Spline functions | Truncation errors | Schroedinger equation | Polynomials | Linearization | Approximation | Nonlinearity | Mathematical models

Journal Article

Engineering Analysis with Boundary Elements, ISSN 0955-7997, 2008, Volume 32, Issue 9, pp. 747 - 756

In this paper the meshless local Petrov–Galerkin (MLPG) method is presented for the numerical solution of the two-dimensional non-linear Schrödinger equation....

Unit Heaviside test function | Moving least square (MLS) approximation | Non-linear Schrödinger equation | Meshless local Petrov–Galerkin (MLPG) method | Meshless local Petrov-Galerkin (MLPG) method | non-linear Schrodinger equation | unit heaviside test function | BOUNDARY-CONDITIONS | PLATES | SIMULATION | meshless local Petrov-Galerkin (MLPG) method | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | SOLIDS | moving least square (MLS) approximation | SUBJECT | WAVE-EQUATION | RADIAL BASIS FUNCTIONS | HEAT-CONDUCTION | THICK | SCHEMES | Finite element method | Approximation | Mathematical analysis | Meshless methods | Nonlinearity | Mathematical models | Schroedinger equation | Two dimensional

Unit Heaviside test function | Moving least square (MLS) approximation | Non-linear Schrödinger equation | Meshless local Petrov–Galerkin (MLPG) method | Meshless local Petrov-Galerkin (MLPG) method | non-linear Schrodinger equation | unit heaviside test function | BOUNDARY-CONDITIONS | PLATES | SIMULATION | meshless local Petrov-Galerkin (MLPG) method | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | SOLIDS | moving least square (MLS) approximation | SUBJECT | WAVE-EQUATION | RADIAL BASIS FUNCTIONS | HEAT-CONDUCTION | THICK | SCHEMES | Finite element method | Approximation | Mathematical analysis | Meshless methods | Nonlinearity | Mathematical models | Schroedinger equation | Two dimensional

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 05/2009, Volume 14, Issue 5, pp. 2034 - 2045

Non-linear Schrödinger equation for optical medias with saturable non-linear refractive index is obtained and numerical calculation method is applied and...

Solitary solutions | Non-linear Schrödinger equation | Non-linear effects | Saturable soliton | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | COLLISION | PHYSICS, MATHEMATICAL | Non-linear Schrodinger equation | REGION | GUIDES | ANOMALOUS-DISPERSION | TRANSMISSION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | BISTABILITY | OPTICAL-FIBERS | INDEX CHANGE | WAVE-PROPAGATION

Solitary solutions | Non-linear Schrödinger equation | Non-linear effects | Saturable soliton | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | COLLISION | PHYSICS, MATHEMATICAL | Non-linear Schrodinger equation | REGION | GUIDES | ANOMALOUS-DISPERSION | TRANSMISSION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | BISTABILITY | OPTICAL-FIBERS | INDEX CHANGE | WAVE-PROPAGATION

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

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

Journal of Electromagnetic Waves and Applications, ISSN 0920-5071, 03/2018, Volume 32, Issue 4, pp. 504 - 515

In this paper, we consider the non-linear Schrödinger equation in fibers with the presence of group velocity dispersion, selfphase modulation and second-order...

The second-order non-linear Schrödinger equation | dark soliton solution | traveling wave solution | Gaussian solution | complexitons solution | bight soliton solution | DARBOUX TRANSFORMATION | BREATHER WAVES | PHYSICS, APPLIED | SYMMETRIES | INFINITE CONSERVATION-LAWS | ROGUE WAVES | BACKLUND TRANSFORMATION | ENGINEERING, ELECTRICAL & ELECTRONIC | ANALYTIC SOLUTIONS | QUASI-PERIODIC WAVES | The second-order non-linear Schrodinger equation | GAUSSIAN SOLITON | RATIONAL CHARACTERISTICS

The second-order non-linear Schrödinger equation | dark soliton solution | traveling wave solution | Gaussian solution | complexitons solution | bight soliton solution | DARBOUX TRANSFORMATION | BREATHER WAVES | PHYSICS, APPLIED | SYMMETRIES | INFINITE CONSERVATION-LAWS | ROGUE WAVES | BACKLUND TRANSFORMATION | ENGINEERING, ELECTRICAL & ELECTRONIC | ANALYTIC SOLUTIONS | QUASI-PERIODIC WAVES | The second-order non-linear Schrodinger equation | GAUSSIAN SOLITON | RATIONAL CHARACTERISTICS

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

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

Optical and Quantum Electronics, ISSN 0306-8919, 11/2016, Volume 48, Issue 11, pp. 1 - 10

In this paper, we investigate the coupled cubic-quintic non-linear Schrödinger equations, which describe the effects of quintic non-linearity on the...

Non-Kerr medium | Bright soliton solutions | Optics, Lasers, Photonics, Optical Devices | Characterization and Evaluation of Materials | Soliton collision | Coupled cubic-quintic non-linear Schrödinger equations | Symbolic computation | Computer Communication Networks | Physics | Electrical Engineering | BISTABLE SOLITONS | BIREFRINGENT FIBERS | Coupled cubic-quintic non-linear Schrodinger equations | WAVE-GUIDES | OPTICS | OPTICAL SOLITONS | SPATIOTEMPORAL DISPERSION | ENGINEERING, ELECTRICAL & ELECTRONIC

Non-Kerr medium | Bright soliton solutions | Optics, Lasers, Photonics, Optical Devices | Characterization and Evaluation of Materials | Soliton collision | Coupled cubic-quintic non-linear Schrödinger equations | Symbolic computation | Computer Communication Networks | Physics | Electrical Engineering | BISTABLE SOLITONS | BIREFRINGENT FIBERS | Coupled cubic-quintic non-linear Schrodinger equations | WAVE-GUIDES | OPTICS | OPTICAL SOLITONS | SPATIOTEMPORAL DISPERSION | ENGINEERING, ELECTRICAL & ELECTRONIC

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

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

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

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

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

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

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

14.
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Travelling wave solutions of the non-linear Schrödinger's equation in non-Kerr law media

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

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

15.
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Time-dependent method for non-linear Schrödinger equations in inverse scattering problems

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

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

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

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

In this article, we prove the existence of infinitely many non-trivial standing wave solutions of the discrete non-linear Schrödinger equation with the...

47J30 | discrete non-linear Schrödinger equation | 39A12 | Palais-Smale condition | 35Q55 | linking theorem | 37L60 | standing wave solution | 35Q51 | 39A70 | 78A40 | Discrete non-linear Schrodinger equation | Linking theorem | Standing wave solution | INFINITY | discrete non-linear Schrodinger equation | MATHEMATICS, APPLIED | GAP SOLITONS | SMOOTHING PROPERTY | STABILITY | BREATHERS | LATTICES | LOCALIZED MODES | Standing waves | Theorems | Infinity | Existence theorems | Nonlinearity | Joining | Schroedinger equation | Linking

47J30 | discrete non-linear Schrödinger equation | 39A12 | Palais-Smale condition | 35Q55 | linking theorem | 37L60 | standing wave solution | 35Q51 | 39A70 | 78A40 | Discrete non-linear Schrodinger equation | Linking theorem | Standing wave solution | INFINITY | discrete non-linear Schrodinger equation | MATHEMATICS, APPLIED | GAP SOLITONS | SMOOTHING PROPERTY | STABILITY | BREATHERS | LATTICES | LOCALIZED MODES | Standing waves | Theorems | Infinity | Existence theorems | Nonlinearity | Joining | Schroedinger equation | Linking

Journal Article

19.
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Analysis for a two-step dispersion scheme for coupled non-linear Schrödinger equations

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

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

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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