Using the previously developed canonical phase space approach applied to the noisy Burgers equation in one dimension, we discuss in detail the growth morphology in terms of nonlinear soliton modes and superimposed linear modes. We moreover analyze the non-Hermitian character of the linear mode spectrum and the associated dynamical pinning, and mode transmutation from diffusive to propagating behavior induced by the solitons. We discuss the anomalous diffusion of growth modes, switching and pathways, correlations in the multisoliton sector, and in detail the correlations and scaling properties in the two-soliton sector.
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http://dx.doi.org/10.1103/PhysRevE.68.026132 | DOI Listing |
Chaos
January 2025
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China.
We demonstrate that fundamental nonlinear localized modes can exist in the Chen-Lee-Liu equation modified by several parity-time (PT) symmetric complex potentials. The explicit formula of analytical solitons is derived from the physically interesting Scarf-II potential, and families of spatial solitons in internal modes are numerically captured under the optical lattice potential. By the spectral analysis of linear stability, we observe that these bright solitons can remain stable across a broad scope of potential parameters, despite the breaking of the corresponding linear PT-symmetric phases.
View Article and Find Full Text PDFLight Sci Appl
January 2025
Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv, Israel.
This item from the News and Views (N&V) category aims to provide a summary of theoretical and experimental results recently published in ref. , which demonstrates the creation of corner modes in nonlinear optical waveguides of the higher-order topological insulator (HOTI) type. Actually, these are second-order HOTIs, in which the transverse dimension of the topologically protected edge modes is smaller than the bulk dimension (it is 2, in the case of optical waveguide) by 2, implying zero dimension of the protected modes, which are actually realized as corner or defect ones.
View Article and Find Full Text PDFHeliyon
November 2024
Laboratory of Research on Advanced Materials and Nonlinear Sciences, Department of Physics, Faculty of Science, University of Buea, P.O. Box 63, Buea, Cameroon.
In the present work, we focus on the longitudinal model of microtubules (MTs) proposed by Satarić et al. (1993) [12], and that considers MT cells to have ferroelectric properties (behaviors) due to dipolar oscillations of dimers within MTs, i.e.
View Article and Find Full Text PDFWe present an approach to generate stable vortex solitons (VSs) in rotating quasi-phase-matched photonic crystals with quadratic nonlinearity. The photonic crystal is introduced with a checkerboard structure, which can be realized using available technology. The VSs are constructed as four-peak vortex modes of two types: rhombuses and squares.
View Article and Find Full Text PDFIn this paper, the dynamics of the circular Airy beam (CAB) in the spatial fractional nonlinear Schrödinger equation (FNLSE) optical system are investigated. The propagation characteristics of CABs modulated by the quadratic phase modulation (QPM) in a Kerr (cubic) nonlinear medium under power function diffractive modulation modes and parabolic potentials are numerically simulated by using a step-by-step Fourier method. Specifically, the threshold for CABs to form solitons in the Kerr medium is controlled by the Lévy index and the QPM coefficient.
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