Physica D: Nonlinear Phenomena最新文献

英文中文

Breathers and mixed oscillatory states near a Turing–Hopf instability in a two–component reaction–diffusion system

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134482

Fahad Al Saadi , Edgar Knobloch , Alexander Meiners , Hannes Uecker

Numerical continuation is used to study the interaction between a finite wave number Turing instability and a zero wave number Hopf instability in a two-species reaction-diffusion model of a semiconductor device. The model admits two such codimension-two interactions, both with a subcritical Turing branch that is responsible for the presence of spatially localized Turing states. The Hopf branch may also be subcritical. We uncover a large variety of spatially extended and spatially localized states in the vicinity of these points and by varying a third parameter show how disconnected branches of time-periodic spatially localized states can be “zipped up” into snaking branches of time-periodic oscillations. These are of two types: a Turing state embedded in an oscillating background, and a breathing Turing state embedded in a non-oscillating background. Stable two-frequency states resembling a mixture of these two states are also identified. Our results are complemented by direct numerical simulations. The findings explain the origin of the large multiplicity of localized steady and oscillatory patterns arising from the Turing–Hopf interaction and shed light on the competition between them.

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引用次数: 0

Hamiltonian Lorenz-like models

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134494

Francesco Fedele , Cristel Chandre , Martin Horvat , Nedjeljka Žagar

The reduced-complexity models developed by Edward Lorenz are widely used in atmospheric and climate sciences to study nonlinear aspect of dynamics and to demonstrate new methods for numerical weather prediction. A set of inviscid Lorenz models describing the dynamics of a single variable in a zonally-periodic domain, without dissipation and forcing, conserve energy but are not Hamiltonian. In this paper, we start from a general continuous parent fluid model, from which we derive a family of Hamiltonian Lorenz-like models through a symplectic discretization of the associated Poisson bracket, which preserves the Jacobi identity. A symplectic-split integrator is also formulated. These Hamiltonian models conserve energy and maintain the nearest-neighbor couplings inherent in the original Lorenz model. As a corollary, we find that the Lorenz-96 model can be seen as a result of a poor discretization of a Poisson fluid bracket. Hamiltonian Lorenz-like models offer promising alternatives to the original Lorenz models, especially for the qualitative representation of non-Gaussian weather extremes and wave interactions, which underscore many phenomena of the climate system.

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引用次数: 0

Stable patterns with jump-discontinuity for a phytoplankton–zooplankton system with both Allee and fear effect

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134481

Conghui Zhang , Jin Lu , Maoxing Liu , Hanzhi Zhang

This paper is concerned with a phytoplankton–zooplankton system with both Allee and fear effect, in which zooplankton species diffuse but phytoplankton species do not diffuse. We show that this system may lead to a novel pattern formation phenomenon, i.e., far-from-the equilibrium patterns with jump discontinuity. Moreover, the

L^{\infty}

-stability of these discontinuous stationary solutions are demonstrated under appropriate conditions. In addition, we explore how diffusion, Allee and fear effect affect the system. Our results illustrate that (i) if both species diffuse, then the origin and the positive equilibrium are stable. Furthermore, no discontinuous stationary solutions exist; (ii) in the absence of Allee effect, the phenomenon of bistability disappears and only the positive equilibrium is stable. Besides, any discontinuous stationary solutions may be unstable; (iii) when excluding fear effects from the system, the density of zooplankton will be changed, more precisely, as fear costs increase, zooplankton population density declines. Finally, a series of numerical simulations are presented to verified the theoretical results

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引用次数: 0

Material coordinate driven time-space scaled models for anomalous water absorption in swelling soils

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134472

Peibo Tian , Yingjie Liang , Ninghu Su

Anomalous water absorption in soils usually causes changes in the volume, structure and related properties of soils, especially in swelling soils. In this paper, time and space scaled models based on the fractal derivatives are introduced in the diffusion equation in the material coordinate to characterize the anomalous absorption of water in swelling soils, and to derive solutions for both cumulative absorption and absorption rates. Interestingly, the cumulative absorptions given by the fractal and fractional derivative models in terms of the material coordinate are the same. The fractal derivative model provides a different physical mechanism compared with the fractional derivative model. The differences and unity of the time and space fractal derivative models are verified by using the experimental data of water absorption in no tillage-soil and Xerochrept soil.

引用次数: 0

SU(2)-Hidden symmetry of two-level media: Propagation of higher-order ultimately short-wave excitations with nonzero angular momenta

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2025.134539

Romuald K.K. Lemoula , Victor K. Kuetche

Following the SU(2)-symmetry analysis, we perform a more detailed investigation of interaction of ultimately short-wave optical solitons with the two-level media within the viewpoint of propagation of higher-order waveguide excitations with nonzero angular momenta. As a result, we derive a new partial differential evolution model system expressed within the Hilbert space while describing the propagation of circularly polarized optical waveguide excitations. Accordingly, we solve the previous Hamiltonian system and address the expression of the one-soliton solution. We hence depict its spectrum which shows the distribution of the wave-frequency for circular polarization with a pulse-profile. Besides, investigating the variations of the electric field of the medium with respect to the population inversion integral, we discuss some typical features which profiles strongly depend upon the wave-frequency of the carrier. Accordingly, we pay particular interests to the ultimately short waveguide excitations while studying their interactions through the two-wave and three-wave depictions, and their shifts characterizing their nonlinear and rotating scattering features. As a result, we find that such features actually represent the elastic interactions between individual wave structures with the soliton properties arising from the interplay between the nonlinearity and the dispersion. We address some physical implications of the results obtained previously.

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引用次数: 0

On tautological flows of partial difference equations

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2025.134533

Zhonglun Cao, Si-Qi Liu, Youjin Zhang

We propose a new analyzing method, which is called the tautological flow method, to analyze the integrability of partial difference equations (P

Δ

Es) based on that of partial differential equations (PDEs). By using this method, we prove that the discrete

q

-KdV equation is a discrete symmetry of the

q

-deformed KdV hierarchy and its bihamiltonian structure, and we also demonstrate how to directly search for continuous symmetries and bihamiltonian structures of P

Δ

Es by using the approximated tautological flows and their quasi-triviality transformation.

引用次数: 0

Modeling the impacts of chemical substances and time delay to mitigate regional atmospheric pollutants and enhance rainfall

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134507

Gauri Agrawal , Alok Kumar Agrawal , A.K. Misra

Rainfall, a crucial process of the hydrological cycle, involves the condensation of atmospheric cloud droplets into raindrops that fall on the Earth’s surface, providing essentials for human well-being and ecosystem. Research studies show that the condensation–nucleation process for forming raindrops is reduced due to atmospheric pollutants. In this scenario, introducing chemical substances may effectively mitigate regional atmospheric pollution, and reduced atmospheric pollution may lead to adequate rainfall. In the present research work, we analyze rainfall dynamics using a modeling approach with the incorporation of a time lag involved between measuring the data for atmospheric pollution and introducing chemical substances in the regional atmosphere. Here, we assume the formation rate of cloud droplets as a decreasing function of atmospheric pollutants. It is also assumed that introducing chemical substances reduces regional atmospheric pollution. Involving time delay as a bifurcation parameter, we analyze the stability, direction, and period of the bifurcating periodic solutions arising through Hopf bifurcation. Along with this, the presented numerical simulations corroborate the analytical results of our mathematical model. The modeling study reveals that the use of chemical substances in proportion to the concentration of atmospheric pollutants measured at time (

t - τ

) becomes crucial to mitigate the atmospheric pollutants because as time delay exceeds a threshold value, the system loses its stability and undergoes Hopf bifurcation.

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引用次数: 0

Generalized and new solutions of the NRT nonlinear Schrödinger equation

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134515

P.R. Gordoa, A. Pickering, D. Puertas-Centeno, E.V. Toranzo

In this paper we present new solutions of the non-linear Schrödinger equation proposed by Nobre, Rego-Monteiro and Tsallis for the free particle, obtained from different Lie symmetry reductions. Analytical expressions for the wave function, the auxiliary field and the probability density are derived using a variety of approaches. Solutions involving elliptic functions, Bessel and modified Bessel functions, as well as the inverse error function are found, amongst others. On the other hand, a closed-form expression for the general solution of the traveling wave ansatz (see Bountis and Nobre) is obtained for any real value of the nonlinearity index. This is achieved through the use of the so-called generalized trigonometric functions as defined by Lindqvist and Drábek, the utility of which in analyzing the equation under study is highlighted throughout the paper.

引用次数: 0

On non-autonomous Hamiltonian dynamics, dual spaces, and kinetic lifts

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134504

Begüm Ateşli , Oğul Esen , Manuel de León , Cristina Sardón

Vlasov kinetic dynamics fits within the Poisson framework, specifically in the Lie–Poisson form. In this context, each particle constituting the plasma follows classical symplectic Hamiltonian motion. More recently, this formulation has been extended to the kinetic formulation of a collection of particles flowing through contact Hamiltonian dynamics.

In this paper, we introduce geometric kinetic theories within the frameworks of cosymplectic and cocontact manifolds, aiming to generalize the existing literature on symplectic kinetic theory and contact kinetic theory to include time-dependent dynamics. The cosymplectic and cocontact kinetic theories are formulated in terms of both momentum variables and density functions. These alternative realizations are connected through Poisson/momentum maps. Furthermore, in cocontact geometry, we present a hierarchical analysis of nine distinct dynamical motions, which serve as various manifestations of Hamiltonian, evolution, and gradient flows.

引用次数: 0

Relativistic effects in the dynamics of a particle in a Coulomb field

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2025.134534

Rafael Ortega , David Rojas

We prove that Bertrand’s property cannot occur in a special-relativistic scenario using the properties of the period function of planar centers. We also explore some integrability properties of the relativistic Coulomb problem and the asymptotic behavior of collision solutions.

引用次数: 0

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