Nonlinear Fourier Analysis: Rogue Waves in Numerical Modeling and Data Analysis
Journal of Marine Science and Engineering, 2020 Nonlinear Fourier Analysis (NLFA) as developed herein begins with the nonlinear Schrödinger equation in two-space and one-time dimensions (the 2+1 NLS equation).
Alfred R. Osborne
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Existence and Stability of standing waves for supercritical NLS with a Partial Confinement [PDF]
, 2016 We prove the existence of orbitally stable ground states to NLS with a partial confinement together with qualitative and symmetry properties. This result is obtained for nonlinearities which are $L^2$-supercritical, in particular we cover the physically ...
Bellazzini, J. +3 more
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Finite Difference Solution Methods for a System of the Nonlinear Schrödinger Equations
Nonlinear Analysis, 2004 This paper investigates finite difference schemes for solving a system of the nonlinear Schrödinger (NLS) equations. Several types of schemes, including explicit, implicit, Hopscotch-type and Crank-Nicholson-type are defined.
A. Kurtinaitis, F. Ivanauskas
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Instability of Double-Periodic Waves in the Nonlinear Schrödinger Equation
Frontiers in Physics, 2021 It is shown how to compute the instability rates for the double-periodic solutions to the cubic NLS (nonlinear Schrödinger) equation by using the Lax linear equations.
Dmitry E. Pelinovsky
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Finite difference scheme for two-dimensional periodic nonlinear Schrödinger equations [PDF]
Journal of evolution equations (Printed ed.), 2019 A nonlinear Schrödinger equation (NLS) on a periodic box can be discretized as a discrete nonlinear Schrödinger equation (DNLS) on a periodic cubic lattice, which is a system of finitely many ordinary differential equations.
Younghun Hong +3 more
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Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation. [PDF]
PLoS ONE, 2018 In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation.
Wei Liu, Jing Zhang, Xiliang Li
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Journal of Applied Mathematics, 2014 The coupled nonlinear Schrödinger (NLS) equations describing power and phase of the optical waves are used to model phase-sensitive (PS) parametric amplification in a width-modulated silicon-on-insulator (SOI) channel waveguide.
Xuefeng Li, Zhaolu Wang, Hongjun Liu
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T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -deformed nonlinear Schrödinger
Journal of High Energy Physics, 2021 The T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -deformed classical Lagrangian of a 2D Lorentz invariant theory can be derived from the original one, perturbed only at first order by the bare T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ composite field ...
Paolo Ceschin +2 more
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Nonlinear Schr{\"o}dinger equation: concentration on circles driven by an external magnetic field [PDF]
, 2015 In this paper, we study the semiclassical limit for the stationary magnetic nonlinear Schr\"odinger equation \begin{align}\label{eq:initialabstract}\left( i \hbar \nabla + A(x) \right)^2 u + V(x) u = |u|^{p-2} u, \quad x\in \mathbb{R}^{3},\end{align ...
Bonheure, Denis +2 more
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Transport of gaussian measures by the flow of the nonlinear Schr\"odinger equation [PDF]
, 2019 We prove a new smoothing type property for solutions of the 1d quintic Schr\"odinger equation. As a consequence, we prove that a family of natural gaussian measures are quasi-invariant under the flow of this equation.
Planchon, F. +2 more
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