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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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 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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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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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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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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Global existence and compact attractors for the discrete nonlinear Schrödinger equation [PDF]
, 1965 We study the asymptotic behavior of solutions of discrete nonlinear Schrödinger-type (DNLS) equations. For a conservative system, we consider the global in time solvability and the question of existence of standing wave solutions.
Karachalios, Nikos I. +1 more
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Semiclassical stationary states for nonlinear Schr\"odinger equations under a strong external magnetic field [PDF]
, 2015 We construct solutions to the nonlinear magnetic Schr\"odinger equation $$ \left\{ \begin{aligned} - \varepsilon^2 \Delta_{A/\varepsilon^2} u + V u &= \lvert u\rvert^{p-2} u & &\text{in}\ \Omega,\\ u &= 0 & &\text{on}\ \partial\Omega, \end{aligned}
Di Cosmo, Jonathan +1 more
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Solitary waves in nonlocal NLS with dispersion averaged saturated nonlinearities [PDF]
, 2017 A nonlinear Schr\"odinger equation (NLS) with dispersion averaged nonlinearity of saturated type is considered. Such a nonlocal NLS is of integro-differential type and it arises naturally in modeling fiber-optics communication systems with periodically ...
Hundertmark, Dirk +3 more
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