UofT Libraries is getting a new library services platform in January 2021.

Learn more about the change.

## Search Articles

J Phys Soc Jpn, ISSN 0031-9015, 12/2012, Volume 81, Issue 12, pp. 124007 - 124007-4

The Fokas--Lenells (FL) equation arises as a model equation which describes for nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order...

Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | Mathematical models | Schrodinger equation | Propagation | Asymptotic methods | Fiber optics | Optical fibers | Wave propagation | Asymptotic properties | Mathematical analysis | Nonlinearity | Transformations | Schroedinger equation | Representations

Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | Mathematical models | Schrodinger equation | Propagation | Asymptotic methods | Fiber optics | Optical fibers | Wave propagation | Asymptotic properties | Mathematical analysis | Nonlinearity | Transformations | Schroedinger equation | Representations

Journal Article

Letters in mathematical physics, ISSN 1573-0530, 10/2018, Volume 109, Issue 4, pp. 945 - 973

Rogue waves in the nonlocal
$${\mathcal {PT}}$$
PT
-symmetric nonlinear Schrödinger (NLS) equation are studied by Darboux transformation...

Geometry | Schur polynomials | 37K35 | Rogue waves | Nonlocal NLS equation | Theoretical, Mathematical and Computational Physics | Complex Systems | 35Q55 | Group Theory and Generalizations | Physics | 35C08 | Darboux transformation | Physical Sciences | Physics, Mathematical | Science & Technology | Water waves | Singularities | Schroedinger equation | Polynomials

Geometry | Schur polynomials | 37K35 | Rogue waves | Nonlocal NLS equation | Theoretical, Mathematical and Computational Physics | Complex Systems | 35Q55 | Group Theory and Generalizations | Physics | 35C08 | Darboux transformation | Physical Sciences | Physics, Mathematical | Science & Technology | Water waves | Singularities | Schroedinger equation | Polynomials

Journal Article

Nonlinear dynamics, ISSN 0924-090X, 1/2016, Volume 83, Issue 1, pp. 731 - 738

...–Milovic equation that serves as a generalized version of the usual nonlinear Schrodinger’s equation. Several integration schemes are implemented to secure solitons and other solutions to the model...

Engineering | Vibration, Dynamical Systems, Control | Biswas–Milovic equation | Integrability | Optical solitons | Mechanics | Automotive Engineering | Mechanical Engineering | Optical fibers | Schroedinger equation | Power law | Solitary waves | Mathematical analysis | Solitons | Nonlinearity | Mathematical models | Cases

Engineering | Vibration, Dynamical Systems, Control | Biswas–Milovic equation | Integrability | Optical solitons | Mechanics | Automotive Engineering | Mechanical Engineering | Optical fibers | Schroedinger equation | Power law | Solitary waves | Mathematical analysis | Solitons | Nonlinearity | Mathematical models | Cases

Journal Article

Journal of mathematical physics, ISSN 1089-7658, 04/2012, Volume 53, Issue 4, pp. 043507 - 043507-7

This paper considers the fractional Schrödinger equation with unbounded potential...

Physical Sciences | Physics | Physics, Mathematical | Science & Technology | Standing waves | Manifolds | Ground state | Schroedinger equation | Lagrange multipliers | Mathematical analysis

Physical Sciences | Physics | Physics, Mathematical | Science & Technology | Standing waves | Manifolds | Ground state | Schroedinger equation | Lagrange multipliers | Mathematical analysis

Journal Article

Journal of dynamics and differential equations, ISSN 1040-7294, 3/2019, Volume 31, Issue 1, pp. 369 - 383

This paper is dedicated to studying the semilinear Schrödinger equation
$$\begin{aligned} \left\{ \begin{array}{ll} -\triangle u+V(x)u=f(x, u), \quad x...

35J20 | Local super-quadratic conditions | Ordinary Differential Equations | 35J60 | Mathematics | Superlinear | Applications of Mathematics | Partial Differential Equations | Schrödinger equation | Asymptotically linear | Physical Sciences | Mathematics, Applied | Science & Technology | Schroedinger equation | Coercivity

35J20 | Local super-quadratic conditions | Ordinary Differential Equations | 35J60 | Mathematics | Superlinear | Applications of Mathematics | Partial Differential Equations | Schrödinger equation | Asymptotically linear | Physical Sciences | Mathematics, Applied | Science & Technology | Schroedinger equation | Coercivity

Journal Article

Manuscripta mathematica, ISSN 0025-2611, 3/2018, Volume 155, Issue 3, pp. 471 - 501

Given a complete, smooth metric measure space $$(M,g,e^{-f}dv)$$
(M,g,e-fdv)
with the Bakry–Émery Ricci curvature bounded from below, various gradient estimates for solutions of the following general f-heat equations...

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 53C21 | Mathematics, general | Algebraic Geometry | 35R01 | Mathematics | Number Theory | 58J35 | Physical Sciences | Science & Technology | Thermodynamics | Nonlinear equations | Schroedinger equation | Mathematical analysis | Curvature

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 53C21 | Mathematics, general | Algebraic Geometry | 35R01 | Mathematics | Number Theory | 58J35 | Physical Sciences | Science & Technology | Thermodynamics | Nonlinear equations | Schroedinger equation | Mathematical analysis | Curvature

Journal Article

Optics letters, ISSN 1539-4794, 03/2015, Volume 40, Issue 6, pp. 1117 - 1120

In quantum mechanics, the space-fractional Schrodinger equation provides a natural extension of the standard Schrodinger equation when the Brownian trajectories in Feynman path integrals are replaced by Levy flights...

Optics | Physical Sciences | Science & Technology | Integrals | Dynamics | Quantum mechanics | Holes | Optical pumping | Schroedinger equation | Laser beams | Standards

Optics | Physical Sciences | Science & Technology | Integrals | Dynamics | Quantum mechanics | Holes | Optical pumping | Schroedinger equation | Laser beams | Standards

Journal Article

Numerical algorithms, ISSN 1572-9265, 12/2017, Volume 79, Issue 1, pp. 337 - 356

In the paper, we first propose a Crank-Nicolson Galerkin-Legendre (CN-GL) spectral scheme for the one-dimensional nonlinear space fractional Schrödinger equation...

Nonlinear space fractional Schrödinger equation | Algorithms | Algebra | Galerkin-Legendre spectral method | Numerical Analysis | Computer Science | Numeric Computing | Theory of Computation | Crank-Nicolson difference method | Convergence analysis | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Accuracy | Spectra | Schroedinger equation | Galerkin method | Numerical methods | Spectral methods

Nonlinear space fractional Schrödinger equation | Algorithms | Algebra | Galerkin-Legendre spectral method | Numerical Analysis | Computer Science | Numeric Computing | Theory of Computation | Crank-Nicolson difference method | Convergence analysis | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Accuracy | Spectra | Schroedinger equation | Galerkin method | Numerical methods | Spectral methods

Journal Article

Journal of scientific computing, ISSN 1573-7691, 11/2013, Volume 60, Issue 2, pp. 390 - 407

In this paper, we study linearized Crank–Nicolson Galerkin FEMs for a generalized nonlinear Schrödinger equation...

Computational Mathematics and Numerical Analysis | Algorithms | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Mathematics | Unconditionally optimal error estimate | Generalized nonlinear Schrödinger equation | Crank–Nicolson Galerkin FEMs | Crank-Nicolson Galerkin FEMs | Physical Sciences | Mathematics, Applied | Science & Technology | Finite element method | Errors | Error analysis | Mathematical models | Schroedinger equation | Estimates | Galerkin methods | Optimization

Computational Mathematics and Numerical Analysis | Algorithms | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Mathematics | Unconditionally optimal error estimate | Generalized nonlinear Schrödinger equation | Crank–Nicolson Galerkin FEMs | Crank-Nicolson Galerkin FEMs | Physical Sciences | Mathematics, Applied | Science & Technology | Finite element method | Errors | Error analysis | Mathematical models | Schroedinger equation | Estimates | Galerkin methods | Optimization

Journal Article

1999, Applied mathematical sciences, ISBN 9780387986111, Volume 139., XVI, 350

eBook

Journal of dynamics and differential equations, ISSN 1572-9222, 08/2015, Volume 29, Issue 3, pp. 1017 - 1030

We study the standing waves of the nonlinear fractional Schrödinger equation. We obtain that when
$$0<\gamma <2s$$
0
<
γ...

Profile decomposition | Ordinary Differential Equations | Nonlinear fractional Schrödinger equation | Orbital stability | Mathematics | Applications of Mathematics | Partial Differential Equations | Standing wave | Physical Sciences | Mathematics, Applied | Science & Technology | Standing waves | Ground state | Schroedinger equation | Solitary waves

Profile decomposition | Ordinary Differential Equations | Nonlinear fractional Schrödinger equation | Orbital stability | Mathematics | Applications of Mathematics | Partial Differential Equations | Standing wave | Physical Sciences | Mathematics, Applied | Science & Technology | Standing waves | Ground state | Schroedinger equation | Solitary waves

Journal Article

Optical and quantum electronics, ISSN 0306-8919, 1/2018, Volume 50, Issue 1, pp. 1 - 10

In this article, we study the unstable nonlinear Schrödinger equation (UNLSE). Analytically by modified extended direct algebraic method, which describes the disturbances in time evolution of marginally stable or unstable media...

Elliptic function solutions | Optics, Lasers, Photonics, Optical Devices | Unstable nonlinear Schrödinger equation | Solitons | Characterization and Evaluation of Materials | Modified extended direct algebraic method | Solitary wave solutions | Computer Communication Networks | Physics | Electrical Engineering | Quantum Science & Technology | Engineering | Physical Sciences | Technology | Engineering, Electrical & Electronic | Optics | Science & Technology | Nonlinear equations | Nonlinear analysis | Nonlinear evolution equations | Schroedinger equation | Elliptic functions | Nonlinear optics | Solitary waves

Elliptic function solutions | Optics, Lasers, Photonics, Optical Devices | Unstable nonlinear Schrödinger equation | Solitons | Characterization and Evaluation of Materials | Modified extended direct algebraic method | Solitary wave solutions | Computer Communication Networks | Physics | Electrical Engineering | Quantum Science & Technology | Engineering | Physical Sciences | Technology | Engineering, Electrical & Electronic | Optics | Science & Technology | Nonlinear equations | Nonlinear analysis | Nonlinear evolution equations | Schroedinger equation | Elliptic functions | Nonlinear optics | Solitary waves

Journal Article

Journal of nonlinear science, ISSN 1432-1467, 11/2017, Volume 28, Issue 2, pp. 739 - 763

The Riemann–Hilbert problem for the coupled nonlinear Schrödinger equation is formulated on the basis of the corresponding $$3\times 3$$
3...

35Q15 | Analysis | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Mathematical and Computational Engineering | Economic Theory/Quantitative Economics/Mathematical Methods | 35Q55 | Long-time asymptotics | Mathematics | 35B40 | Riemann–Hilbert problem | Coupled nonlinear Schrödinger equation | Physical Sciences | Technology | Physics, Mathematical | Mechanics | Mathematics, Applied | Physics | Science & Technology | Steepest descent method | Schroedinger equation | Cauchy problem

35Q15 | Analysis | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Mathematical and Computational Engineering | Economic Theory/Quantitative Economics/Mathematical Methods | 35Q55 | Long-time asymptotics | Mathematics | 35B40 | Riemann–Hilbert problem | Coupled nonlinear Schrödinger equation | Physical Sciences | Technology | Physics, Mathematical | Mechanics | Mathematics, Applied | Physics | Science & Technology | Steepest descent method | Schroedinger equation | Cauchy problem

Journal Article

Probability theory and related fields, ISSN 0178-8051, 12/2017, Volume 169, Issue 3, pp. 1121 - 1168

We consider the cubic fourth order nonlinear Schrödinger equation on the circle. In particular, we prove that the mean-zero Gaussian measures on Sobolev spaces
$$H^s({\mathbb {T}})$$
H
s
(
T
)
,
$$s > \frac{3}{4...

Quasi-invariance | Gaussian measure | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Biharmonic nonlinear Schrödinger equation | 35Q55 | Probability Theory and Stochastic Processes | Mathematics | Fourth order nonlinear Schrödinger equation | Quantitative Finance | Statistics & Probability | Physical Sciences | Science & Technology | Sobolev space | Schroedinger equation | Invariants

Quasi-invariance | Gaussian measure | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Biharmonic nonlinear Schrödinger equation | 35Q55 | Probability Theory and Stochastic Processes | Mathematics | Fourth order nonlinear Schrödinger equation | Quantitative Finance | Statistics & Probability | Physical Sciences | Science & Technology | Sobolev space | Schroedinger equation | Invariants

Journal Article