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   Articles with "nonlinear schr" as a keyword



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Global dynamics for a class of inhomogeneous nonlinear Schrödinger equations with potential

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recommendations! Published in 2021 at "Mathematische Nachrichten"

DOI: 10.1002/mana.201900427

Abstract: We consider a class of L2‐supercritical inhomogeneous nonlinear Schrödinger equations with potential in three dimensions. In the focusing case, using a recent method of Dodson and Murphy, we first study the energy scattering below the… read more here.

Keywords: class; equations potential; nonlinear schr; inhomogeneous nonlinear ... See more keywords
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Characteristics of rogue waves on a soliton background in a coupled nonlinear Schrödinger equation

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recommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.5532

Abstract: In this paper, a coupled nonlinear Schrödinger (CNLS) equation, which can describe evolution of localized waves in a two‐mode nonlinear fiber, is under investigation. By using the Darboux‐dressing transformation, the new localized wave solutions of… read more here.

Keywords: coupled nonlinear; waves soliton; nonlinear schr; rogue waves ... See more keywords
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Rational and semi‐rational solutions of a nonlocal (2 + 1)‐dimensional nonlinear Schrödinger equation

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recommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.5792

Abstract: We consider the fully parity‐time (PT) symmetric nonlocal (2 + 1)‐dimensional nonlinear Schrödinger (NLS) equation with respect to x and y. By using Hirota's bilinear method, we derive the N‐soliton solutions of the nonlocal NLS… read more here.

Keywords: semi rational; rational solutions; nonlocal dimensional; nonlinear schr ... See more keywords
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Exact traveling wave solutions for resonance nonlinear Schrödinger equation with intermodal dispersions and the Kerr law nonlinearity

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recommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.5827

Abstract: The main aim of this article is to present some new exact solutions of the resonant nonlinear Schrödinger equation. These solutions are derived by using the generated exponential rational function method (GERFM). The kink‐type, bright,… read more here.

Keywords: dinger equation; schr dinger; nonlinear schr;
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The N‐coupled higher‐order nonlinear Schrödinger equation: Riemann‐Hilbert problem and multi‐soliton solutions

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recommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.6055

Abstract: In this work, the Riemann‐Hilbert (RH) problem of the N‐coupled high‐order nonlinear Schrödinger (N‐CHNLS) equations is studied carefully, which controls the propagation of N fields with all high‐order effects such as high‐order dispersion, self‐steepening effect,… read more here.

Keywords: hilbert problem; order; order nonlinear; problem ... See more keywords
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A note on the finite fractal dimension of the global attractors for dissipative nonlinear Schrödinger‐type equations

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recommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.6709

Abstract: In this article, we present, throughout two basic models of damped nonlinear Schrödinger (NLS)–type equations, a new idea to bound from above the fractal dimension of the global attractors for NLS‐type equations. This could answer… read more here.

Keywords: schr dinger; type equations; fractal dimension; nonlinear schr ... See more keywords
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Abundant exact solutions to a generalized nonlinear Schrödinger equation with local fractional derivative

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recommendations! Published in 2021 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.7302

Abstract: The paper aims to employ a new effective methodology to build exact fractional solutions to the generalized nonlinear Schrödinger equation with a local fractional operator defined on Cantor sets. The equation contains group velocity dispersion… read more here.

Keywords: generalized nonlinear; nonlinear schr; solutions generalized; equation ... See more keywords
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Strong instability of solitary waves for inhomogeneous nonlinear Schrödinger equations

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recommendations! Published in 2021 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.7731

Abstract: This paper studies the inhomogeneous nonlinear Schrödinger equations, which may model the propagation of laser beams in nonlinear optics. Using the cross‐constrained variational method, a sharp condition for global existence is derived. Then, by solving… read more here.

Keywords: instability solitary; nonlinear schr; strong instability; inhomogeneous nonlinear ... See more keywords
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On Fourier time-splitting methods for nonlinear Schrödinger equations in the semi-classical limit II. Analytic regularity

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recommendations! Published in 2017 at "Numerische Mathematik"

DOI: 10.1007/s00211-016-0841-y

Abstract: We consider the time discretization based on Lie-Trotter splitting, for the nonlinear Schrödinger equation, in the semi-classical limit, with initial data under the form of WKB states. We show that both the exact and the… read more here.

Keywords: nonlinear schr; classical limit; time; semi classical ... See more keywords
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Maximal amplitudes of finite-gap solutions for the focusing Nonlinear Schrödinger Equation

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recommendations! Published in 2017 at "Communications in Mathematical Physics"

DOI: 10.1007/s00220-017-2895-9

Abstract: AbstractFinite-gap (algebro-geometric) solutions to the focusing Nonlinear Schrödinger Equation (fNLS) 0-1$$i \psi_t + \psi_{xx} + 2|\psi|^2\psi=0,$$iψt+ψxx+2|ψ|2ψ=0,are quasi-periodic solutions that represent nonlinear multi-phase waves. In general, a finite-gap solution for (0-1) is defined by a collection… read more here.

Keywords: dinger equation; nonlinear schr; schr dinger; finite gap ... See more keywords

Scattering for Stochastic Nonlinear Schrödinger Equations

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recommendations! Published in 2019 at "Communications in Mathematical Physics"

DOI: 10.1007/s00220-019-03429-0

Abstract: We study the scattering behavior of global solutions to stochastic nonlinear Schrödinger equations with linear multiplicative noise. In the case where the quadratic variation of the noise is globally finite and the nonlinearity is defocusing,… read more here.

Keywords: stochastic nonlinear; nonlinear schr; schr dinger; dinger equations ... See more keywords