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The nonlinear Schr{\"o}odinger (NLS) equation, which incorporates higher-order dispersive terms, is widely employed in the theoretical analysis of various physical phenomena. In this study, we explore the non-commutative extension of the…

Mathematical Physics · Physics 2023-11-13 H. W. A. Riaz , J. Lin

We investigate the long-time evolution of weakly perturbed single-site breathers (localized stationary states) in the discrete nonlinear Schroedinger (DNLS) equation. The perturbations we consider correspond to time-periodic solutions of…

Pattern Formation and Solitons · Physics 2009-10-31 Magnus Johansson , Serge Aubry

We consider a nonlinear Klein-Gordon equation with a quasilinear quadratic term. The Nonlinear Schr\"odinger (NLS) equation can be derived as a formal approximation equation describing the evolution of the envelopes of slowly modulated…

Analysis of PDEs · Mathematics 2017-08-23 Wolf-Patrick Düll

Nonlinear instability and refraction by ocean currents are both important mechanisms that go beyond the Rayleigh approximation and may be responsible for the formation of freak waves. In this paper, we quantitatively study nonlinear effects…

Fluid Dynamics · Physics 2012-08-21 L. H. Ying , L. Kaplan

From among the waves whose dynamics are governed by the nonlinear Schr\"odinger (NLS) equation, we find a robust, spatiotemporally disordered family, in which waves initialized with increasing amplitudes, on average, over long time scales,…

Pattern Formation and Solitons · Physics 2021-07-05 Katelyn Plaisier Leisman , Douglas Zhou , J. W. Banks , Gregor Kovačič , David Cai

In this paper, we characterize a family of solitary waves for NLS with derivative (DNLS) by the structue analysis and the variational argument. Since (DNLS) doesn't enjoy the Galilean invariance any more, the structure analysis here is…

Analysis of PDEs · Mathematics 2019-06-12 Changxing Miao , Xingdong Tang , Guixiang Xu

We measure spectra, spatial correlation functions and probability density functions (PDFs) for waves amplitudes for generalized one-dimensional nonlinear Schrodinger (NLS) equation of focusing type with saturated nonlinearity. All…

Optics · Physics 2013-10-18 D. S. Agafontsev

We study the periodic traveling wave solutions of the derivative nonlinear Schr\"{o}dinger equation (DNLS). It is known that DNLS has two types of solitons on the whole line; one has exponential decay and the other has algebraic decay. The…

Analysis of PDEs · Mathematics 2025-02-27 Masayuki Hayashi

The fractional discrete nonlinear Schr\"odinger equation (fDNLS) is studied on a periodic lattice from the analytic and dynamic perspective by varying the mesh size $h>0$ and the nonlocal L\'evy index $\alpha \in (0,2]$. We show that the…

Analysis of PDEs · Mathematics 2025-10-16 Brian Choi

Nonlinear acoustic evolution is often discussed in the context of wave-steepening that leads to shock formation, and is of special interest in applications where the shock continues to strengthen due to a narrowing of its channel or the…

Fluid Dynamics · Physics 2023-12-27 Tamar Faran , Christopher D. Matzner , Eliot Quataert

We consider the problem of existence and stability of solitary traveling waves for the one dimensional discrete non linear Schroedinger equation (DNLS) with cubic nonlinearity, near the continuous limit.We construct a family of solutions…

Numerical Analysis · Mathematics 2018-05-10 Joackim Bernier , Erwan Faou

We study the periodic cubic derivative non-linear Schr\"odinger equation (dNLS) and the (focussing) quintic non-linear Schr\"odinger equation (NLS). These are both $L^2$ critical dispersive models, which exhibit threshold type behavior,…

Analysis of PDEs · Mathematics 2021-05-12 Sevdzhan Hakkaev , Milena Stanislavova , Atanas Stefanov

We study a three-wave truncation of the high-order nonlinear Schr\"odinger equation for deepwater waves (HONLS, also named Dysthe equation). We validate our approach by comparing it to numerical simulation, distinguish the impact of the…

Fluid Dynamics · Physics 2017-08-02 Andrea Armaroli , Maura Brunetti , Jérôme Kasparian

We report the theoretical derivation and the experimental as well as numerical observation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of…

Pattern Formation and Solitons · Physics 2018-06-06 F. Tsitoura , U. Gietz , A. Chabchoub , N. Hoffmann

We study weakly nonlinear wave perturbations propagating in a cold nonrelativistic and magnetized ideal quark-gluon plasma. We show that such perturbations can be described by the Ostrovsky equation. The derivation of this equation is…

High Energy Physics - Phenomenology · Physics 2019-12-17 D. A. Fogaça , R. Fariello , F. S. Navarra , Y. A. Stepanyants

We elaborate a fractional discrete nonlinear Schr\"{o}dinger (FDNLS) equation based on an appropriately modified definition of the Riesz fractional derivative, which is characterized by its L\'{e}vy index (LI). This FDNLS equation…

Pattern Formation and Solitons · Physics 2024-09-04 Ming Zhong , Boris A. Malomed , Zhenya Yan

This paper delves into the study of multi-component derivative nonlinear Schrodinger (n-DNLS) equations featuring nonzero boundary conditions. Employing the Darboux transformation (DT) method, we derive higher-order vector rogue wave…

Exactly Solvable and Integrable Systems · Physics 2023-12-20 Lin Huian , Ling Liming

The existence of nonzero periodic travelling wave solutions for a general discrete nonlinear Schr\"odinger equation (DNLS) on finite one-dimensional lattices is proved. The DNLS features a general nonlinear term and variable range of…

Dynamical Systems · Mathematics 2017-11-08 Dirk Hennig

We construct space quasi-periodic standing wave solutions to the nonlinear Schr\"odinger equations on R^d for arbitrary d. This is a type of quasi-periodic nonlinear Bloch-Floquet waves.

Analysis of PDEs · Mathematics 2020-04-30 W. -M. Wang

As a formal approximation, the nonlinear Schr\"{o}dinger (NLS) equation can be derived to describe the evolution of the envelopes of small oscillating wave packets-like solutions to the Euler-Poisson system. In this paper we rigorously…

Analysis of PDEs · Mathematics 2025-12-09 Huimin Liu , Xueke Pu