Physica D: Nonlinear Phenomena最新文献

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Dynamics of nonlinear waves in a low-pass reaction diffusion electrical network and some exact and implicit Modulated compact solutions

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2025.134532

William Kamgaing Mabou , Désiré Ndjanfang , Nkeh Oma Nfor , Muluh Fombu Andrew , Fabien Kenmogne , Hatou-Yvelin Donkeng , David Yemélé

In this paper, we analytically investigate the dynamic behavior of the extended nonlinear Schrödinger (ENLS) equation. This equation describes the propagation of the modulated waves in the network characterized by the nonlinear resistance (NLR) by using the rotative waves approximation. Based on the theory of singular systems and investigating the dynamical behavior of the network, we obtain bifurcations of the phase portraits of the system under different parameter conditions. The result of this qualitative investigation indicates the existence of the nonlinear localized waves with linear phase shift, such as bright pulses, peak pulses, dark pulses, compact dark and compact pulses solitary waves. These nonlinear localized waves can be used in signal processing, electronic devices, and ultra-fast metrology. We derive possible exact explicit and implicit solutions propagating in the nonlinear low-pass electrical transmission line with nonlinear dispersion depending on the frequency range of the chosen carrier wave, for physically realistic parameters.

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引用次数: 0

The inverse problem for periodic travelling waves of the linear 1D shallow-water 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.2024.134496

Robert Hakl , Pedro J. Torres

For the linear 1D shallow-water system with a variable bottom profile, we study the inverse problem of the existence of a periodic bottom profile that allows a periodic travelling wave with prescribed amplitude

q (x)

引用次数: 0

Propagation dynamics in epidemic models with two latent classes

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134509

Guo Lin

This article is concerned with the propagation dynamics in diffusive epidemic models that involve two classes of latent individuals. We formulate the spatial expansion process of latent and infected classes in terms of spreading speeds of initial value problems and minimal wave speed of traveling wave solutions. With several kinds of decaying initial conditions, different leftward and rightward spreading speeds are obtained by constructing proper auxiliary systems. To prove the existence of traveling wave solutions, we use the recipes of generalized upper and lower solutions, the theory of asymptotic spreading as well as a limit process. Our conclusions imply that when the basic reproduction ratio of the corresponding ODEs is larger than the unit, the disease has a minimal spatial expansion speed that equals to the minimal wave speed. When the ratio is not larger than the unit, the disease vanishes and there is not a nontrivial traveling wave solution.

引用次数: 0

High-order optical rogue waves in two coherently coupled nonlinear Schrödinger 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.2025.134538

Juan-Juan Qi, Deng-Shan Wang

In this paper, starting from the matrix nonlinear Schrödinger equation that describes Bose–Einstein condensation, we derive two coherently coupled nonlinear Schrödinger equations via two distinct reductions. Subsequently, we construct the

N

-fold generalized Darboux transformation to investigate the high-order rogue wave solutions of the two equations based on their non-zero seed solutions. Furthermore, the dynamical behaviors of these exact rogue wave solutions are explicitly described graphically. Unlike the well-known eye-shaped and four-petaled rogue waves observed in Manakov equation, some novel behaviors of nonlinear dynamics in these coherently coupled systems are discovered. Additionally, we investigate the asymptotic behavior of the second-order rogue wave solutions and the mixed interaction structures. The findings of this work will contribute to the investigation of optical rogue waves in optical fibers with coherent effects.

引用次数: 0

Nonlinear characteristics of various local waves on nonzero backgrounds of a (2+1)-dimensional generalized Kadomtsev–Petviashvili equation with variable coefficients

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134501

Na Lv , Jiaping Sun , Runfa Zhang , Xuegang Yuan , Yichao Yue

In this paper, a (2+1)-dimensional generalized Kadomtsev–Petviashvili (KP) equation with variable coefficients is studied by the symmetry transformation and bilinear neural network method. By constructing the “3-3-1” neural network models, various important analytical solutions of the equation are successfully obtained, including the breather wave solutions, rogue wave solutions and interaction solutions. Then the evolution behaviors of these analytical solutions are analyzed through selecting appropriate parameters and 3D animations. Specially, three interesting interaction phenomena are presented, i.e., the rogue waves are generated from two moving solitary waves, which have different evolution behaviors on different nonzero background waves. The study of various local waves is helpful to understand the dynamic characteristics of the nonlinear waves, and may be further applied in the fields of scientific research and engineering practice. This paper is used to provide the theoretical guidance and references for the research of studying the evolutions of nonlinear waves in optics, fluid mechanics, and other fields.

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引用次数: 0

Mathematical modeling of trend cycle: Fad, fashion and classic

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134500

Hyeong-Ohk Bae , Seung Yeon Cho , Jane Yoo , Seok-Bae Yun

In this work, we suggest a system of differential equations that models the formulation and evolution of a trend cycle through the consideration of underlying dynamics between the trend participants. Our model captures the five stages of a trend cycle, namely, the onset, rise, peak, decline, and obsolescence. It also provides a unified mathematical criterion/condition to characterize the fad, fashion and classic. We prove that the solution of our model can capture various trend cycles. Numerical simulations are provided to show the expressive power of our model.

引用次数: 0

Breaking of mirror symmetry reshapes vortices in chiral nematic liquid crystals

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2025.134546

Sebastián Echeverría-Alar , Marcel G. Clerc

Nematic liquid crystals offer a rich playground to explore the nonlinear interaction between light and matter. This richness is significantly expanded when nematic liquid crystals are doped with chiral molecules. In simple words, a favorable twist is introduced at a mesoscopic scale in the system, which is manifested through a characteristic length scale, the helical pitch. A classical controlled experiment to observe the response of chiral nematic liquid crystals to external stimuli, is to fill a liquid crystal cell and apply a continuous electrical current. The aftermath will depend on a balance between the elastic and electric properties of the material, the amplitude and frequency of the electric signal, and the competition between the helical pitch and the cell thickness. Although this balance have been studied experimentally and numerically to some extent, the theoretical side of it has been underexplored. In this work, using weakly nonlinear analysis, we derive from first principles a supercritical Ginzburg–Landau type of equation, enabling us to determine theoretically the intricate balance between physical properties that govern the emergence of some chiral textures in the system. Specifically, we focus on how positive and negative vortex solutions of a real cubic Ginzburg–Landau equation are affected by the presence of chirality. We use numerical simulations to show that +1 vortices undergo isotropic stretching, while -1 vortices experience anisotropic deformation, which can be inferred from the free energy of the system. These deformations are in agreement with previous experimental observations. Additionally, we show that it is possible to break the monotonous spatial profile of positive vortices in the presence of chirality.

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引用次数: 0

Stability analysis of a charged particle subject to two non-stationary currents

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2025.134535

Stefano Marò, Francisco Prieto-Castrillo

We study the non relativistic motions of a charged particle in the electromagnetic field generated by two parallel electrically neutral vertical wires carrying time depends currents. Under quantitative conditions on the currents we prove the existence of a vertical strip of stable motions of the particle. The stable strip is contained in the plane of the two wires and the stability is understood in a stronger sense than the isoenergetic stability of Hamiltonian systems. Actually, also variations of the integral given by the linear momentum will be allowed.

引用次数: 0

Exploring population oscillations: Cross-coupling and dispersal effects in prey–predator dynamics

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2025.134525

Debjani Mondal , Moitri Sen , Deeptajyoti Sen

In this investigation, we explore the dynamics of a predator–prey metapopulation model with two identical patches, emphasizing the coupling mechanism through the predators’ dispersal. The coupling mechanism is a particular case of nearest-neighbor coupling, defined by cross-predation, which depicts the fact that the predators have alternative food resources. The study focuses on how dispersion rates and cross-predation affect species coexistence and system dynamics induced by different kinds of bifurcations associated with periodic orbits and stable states. We examined the structural organization of attractors using bifurcation theory and discovered a variety of intricate dynamics, such as symmetric, asymmetric, boundary, and asynchronous attractors. The onset of synchronous and asynchronous dynamical attractors associated with periodic orbits are analyzed by varying the level of coupling strength and the degree of dispersal rates. Another intriguing phenomenon that occurs in our system is the formation of chaotic attractors with asymmetric dynamics from quasi-periodicity as a result of the Neimark-Sacker (NS) bifurcation. We elucidate the emergence and suppression of chaos using the Poincare return map concept. Our system also exhibits intriguing phenomena, such as bistability and multistability, which indicate that it is capable of preserving ecological diversity and enhancing the level of population persistence. Finally, our findings demonstrate that the system’s dynamics are substantially diverse when the dispersal rate is low with limited coupling strengths. The conclusions have a significant impact on the fields of population and evolution science, improving our knowledge of the complex dynamics found in dispersed ecosystems.

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引用次数: 0

Analyzing the impact of proliferation and treatment parameters on low-grade glioma growth using mathematical 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.2024.134491

M. Bodnar , M. Vela-Pérez , A. Tryniecka-Maciążek

Low-grade gliomas (LGGs) are characterized by their slow growth and infiltrative nature, making complete surgical resection challenging and often resulting in the need for adjunctive therapies. This study introduces a mathematical model appeared in Ribba et al. (2012) aimed at elucidating the growth patterns of LGGs and their response to chemotherapy. Our model undergoes validation against clinical data, demonstrating its efficacy in accurately describing real patient data. Through mathematical analysis, we establish the existence of a unique non-negative solution and delve into the stability of steady-state solutions. Notably, we establish the global stability of a tumor-free equilibrium under conditions of sufficiently robust constant and asymptotically dynamics in the case of periodic treatment. Additionally, a sensitivity analysis highlights the proliferation rate as the primary determinant of model outcomes. Finally, numerical simulations are employed to explore the stability of the fitting procedure.

引用次数: 0

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