Article
Mathematics, Applied
Corrado Lattanzio, Delyan Zhelyazov
Summary: This paper investigates the spectral stability of traveling wave solutions to 1D quantum hydrodynamics system with nonlinear viscosity in the (rho,u) variables. A sufficient condition for the stability of the essential spectrum is derived, and the maximum modulus of eigenvalues with non-negative real part is estimated. Numerical computations of the Evans function are also presented to provide numerical evidence of point spectrum stability in a sufficiently large domain of the unstable half-plane.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2021)
Article
Computer Science, Interdisciplinary Applications
Yaming Chen, Xiaogang Deng
Summary: In this paper, we propose nonlinear weights for shock capturing schemes to achieve optimal high order regardless of the order of the critical point. We validate the performance of the proposed nonlinear weights using a fifth-order weighted compact nonlinear scheme and compare the spectral property with existing nonlinear weights. The advantages of the proposed method are validated through various benchmark examples.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Physics, Fluids & Plasmas
L. F. Calazans de Brito, A. M. Kamchatnov
Summary: It is shown that the number of solitons produced from an arbitrary initial pulse of the simple wave type can be analytically calculated if the evolution is governed by a generalized nonlinear Schrodinger equation and the number is large enough. This result generalizes the asymptotic formula derived for completely integrable nonlinear wave equations through the use of the inverse scattering transform method.
Article
Physics, Fluids & Plasmas
Mark J. Ablowitz, Justin T. Cole, Pipi Hu, Peter Rosenthal
Summary: The Peierls-Nabarro barrier is a common effect in discrete nonlinear systems, but topologically protected edge modes in a periodic honeycomb lattice are shown to be unaffected by it, while non-topological modes do slow down and eventually stop propagating. This study provides insight into the nature and application of nonlinear topological insulators.
Article
Mathematics, Applied
Katelyn Plaisier Leisman, Jared C. Bronski, Mathew A. Johnson, Robert Marangell
Summary: In this paper, a rigorous modulational stability theory for periodic traveling wave solutions to equations of nonlinear Schrodinger type is presented. The study focuses on the Jordan structure of the linearization operator and the general properties of the kernel to determine the modulational stability of the underlying periodic traveling wave. The results provide explicit conditions for the generic Jordan form and a normal form for the small eigenvalues resulting from the break-up of the generalized kernel.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2021)
Article
Physics, Fluids & Plasmas
Jonathan A. D. Wattis
Summary: This study proposes a model for a chain of particles coupled by nonlinear springs, in which each mass has an internal mass and all interactions are assumed to be nonlinear. The paper demonstrates how to construct an asymptotic solution using multiple timescales and a consistency condition. The results show that the dynamics are governed by NLS for certain combinations of nonlinearity, but a Ginzburg-Landau equation is obtained when both nonlinearities have quadratic components.
Article
Mathematics, Applied
Sathyanarayanan Chandramouli, Nicholas Ossi, Ziad H. Musslimani, Konstantinos G. Makris
Summary: This paper explores dispersive hydrodynamics associated with the non-Hermitian non-linear Schrödinger equation and obtains a set of dispersive hydrodynamic equations with additional source terms that alter the density and momentum equations. The study focuses on a class of Wadati-type complex potentials and identifies non-Hermitian potentials that lead to modulationally stable constant intensity states. An initial value problem related to a Riemann problem is constructed and studied, which allows the interpretation of the underlying non-Hermitian Riemann problem in terms of an 'optical flow' over an obstacle. The resulting long-time dynamics exhibit a dependence on the location of the step relative to the potential, leading to the formation of diverse nonlinear wave patterns.
Article
Engineering, Ocean
Fazlolah Mohaghegh, Jayathi Murthy, Mohammad-Reza Alam
Summary: The authors have successfully overcome the challenges in predicting ocean waves by utilizing advanced machine learning techniques and a new concept of convolution. Their methodology can predict ocean surface gravity waves more than two orders of magnitude faster than traditional numerical methods, with high accuracy.
APPLIED OCEAN RESEARCH
(2021)
Article
Mechanics
C. D. Matzner, S. Ro
Summary: In studying linear and nonlinear waves, we applied invariant theory and successfully predicted some characteristics of the waves. By introducing adiabatic invariants, we can accurately predict the evolution of waves. We also found fully nonlinear solutions in certain specific problems.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Physics, Applied
MuhibUr Rahman, Ke Wu
Summary: This paper presents a comprehensive analysis of pulse compression capability in hybrid and gyromagnetic non-linear transmission lines (NLTLs). Theoretical analysis and experimental validation are conducted to investigate the parameters responsible for pulse sharpening and compression capability in both hybrid and gyromagnetic NLTLs. The research provides a fresh and successful debut for investigating the effects of gyromagnetic and hybrid NLTLs on pulse compression for future ultrafast electronic systems and interconnects.
JOURNAL OF APPLIED PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Yu Lin, Yaming Chen, Xiaogang Deng
Summary: A fifth-order nonlinear spectral difference method is developed in this paper for solving hyperbolic conservation laws, with a focus on avoiding instability caused by the Gibbs phenomenon arising from interpolation across discontinuities. The proposed method demonstrates accuracy and effectiveness through numerical results.
COMPUTERS & FLUIDS
(2021)
Article
Mechanics
Pranav Thakare, Vineeth Nair, Krishnendu Sinha
Summary: The linear interaction analysis (LIA) method has limitations in studying the interaction between vorticity waves and shock waves, especially for cases with large vorticity wave amplitudes, high incidence angles, and large shock wave curvatures. However, the weakly nonlinear analysis can accurately predict the nonlinear effects and provide the correct scaling of these effects.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Mathematics, Interdisciplinary Applications
A. B. Togueu Motcheyo, J. E. Macias-Diaz
Summary: In this paper, a model for a cross-stitch lattice with onsite nonlinearity is studied and the linear analysis and determination of the homoclinic threshold for this model are carried out theoretically. It is demonstrated that the traveling bandgap soliton is possible as a result of periodic excitation of the edge of the chains in the case of self-focusing nonlinearity. Contrary to the usual supratransmission phenomenon, traveling solitons can be generated by driving the lattice with zero frequency and constant amplitude. Heteroclinic orbit is obtained with the frequency within the phonon band in the case of defocusing nonlinearities, and a traveling phonon kink is obtained by exciting one component of complex waves. The fly phonon breather is observed when driving two complex waves with zero phonon and nonzero phonon frequencies, respectively. The collision between waves from the flat band and phonon band leads to the generation of traveling bright carry by the traveling kink. These results are obtained through computer simulations.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Zhiqiang Cai, Jingshuang Chen, Min Liu
Summary: A least-squares neural network method was developed for solving scalar linear and nonlinear hyperbolic conservation laws by using ReLU neural network as the approximation functions. The method overcomes the difficulty of numerical or automatic differentiation and avoids penalization of artificial viscosity by introducing a new discrete divergence operator. Numerical tests show that the method can accurately compute physical solutions for various benchmark problems without oscillation or smearing.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Multidisciplinary Sciences
Marius Jurgensen, Sebabrata Mukherjee, Mikael C. Rechtsman
Summary: The topological protection of wave transport can apply broadly to different physical platforms and may behave differently in non-linear cases, where quantized transport can still be induced. The concept of a Thouless pump in a one-dimensional model captures the topological quantization of transport, showing that nonlinearity and interactions can induce quantized topological behavior in wave systems.
Article
Mathematics, Applied
Melanie Kobras, Valerio Lucarini, Maarten H. P. Ambaum
Summary: In this study, a minimal dynamical system derived from the classical Phillips two-level model is introduced to investigate the interaction between eddies and mean flow. The study finds that the horizontal shape of the eddies can lead to three distinct dynamical regimes, and these regimes undergo transitions depending on the intensity of external baroclinic forcing. Additionally, the study provides insights into the continuous or discontinuous transitions of atmospheric properties between different regimes.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Shu-hong Xue, Yun-yun Yang, Biao Feng, Hai-long Yu, Li Wang
Summary: This research focuses on the robustness of multiplex networks and proposes a new index to measure their stability under malicious attacks. The effectiveness of this method is verified in real multiplex networks.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Julien Nespoulous, Guillaume Perrin, Christine Funfschilling, Christian Soize
Summary: This paper focuses on optimizing driver commands to limit energy consumption of trains under punctuality and security constraints. A four-step approach is proposed, involving simplified modeling, parameter identification, reformulation of the optimization problem, and using evolutionary algorithms. The challenge lies in integrating uncertainties into the optimization problem.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Alain Bourdier, Jean-Claude Diels, Hassen Ghalila, Olivier Delage
Summary: In this article, the influence of a turbulent atmosphere on the growth of modulational instability, which is the cause of multiple filamentation, is studied. It is found that considering the stochastic behavior of the refractive index leads to a decrease in the growth rate of this instability. Good qualitative agreement between analytical and numerical results is obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Ling An, Liming Ling, Xiaoen Zhang
Summary: In this paper, an integrable fractional derivative nonlinear Schrodinger equation is proposed and a reconstruction formula of the solution is obtained by constructing an appropriate Riemann-Hilbert problem. The explicit fractional N-soliton solution and the rigorous verification of the fractional one-soliton solution are presented.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Marzia Bisi, Nadia Loy
Summary: This paper proposes and investigates general kinetic models with transition probabilities that can describe the simultaneous change of multiple microscopic states of the interacting agents. The mathematical properties of the kinetic model are proved, and the quasi-invariant asymptotic regime is studied and compared with other models. Numerical tests are performed to demonstrate the time evolution of distribution functions and macroscopic fields.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Carlos A. Pires, David Docquier, Stephane Vannitsem
Summary: This study presents a general theory for computing information transfers in nonlinear stochastic systems driven by deterministic forcings and additive and/or multiplicative noises. It extends the Liang-Kleeman framework of causality inference to nonlinear cases based on information transfer across system variables. The study introduces an effective method called the 'Causal Sensitivity Method' (CSM) for computing the rates of Shannon entropy transfer between selected causal and consequential variables. The CSM method is robust, cheaper, and less data-demanding than traditional methods, and it opens new perspectives on real-world applications.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Feiting Fan, Minzhi Wei
Summary: This paper focuses on the existence of periodic and solitary waves for a quintic Benjamin-Bona-Mahony (BBM) equation with distributed delay and diffused perturbation. By transforming the corresponding traveling wave equation into a three-dimensional dynamical system and applying geometric singular perturbation theory, the existence of periodic and solitary waves are established. The uniqueness of periodic waves and the monotonicity of wave speed are also analyzed.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Wangbo Luo, Yanxiang Zhao
Summary: We propose a generalized Ohta-Kawasaki model to study the nonlocal effect on pattern formation in binary systems with long-range interactions. In the 1D case, the model displays similar bubble patterns as the standard model, but Fourier analysis reveals that the optimal number of bubbles for the generalized model may have an upper bound.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Corentin Correia, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas
Summary: The emergence of clustering of rare events is due to periodicity, where fast returns to target sets lead to a bulk of high observations. In this research, we explore the potential of a new mechanism to create clustering of rare events by linking observable functions to a finite number of points belonging to the same orbit. We show that with the right choice of system and observable, any given cluster size distribution can be obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Enyu Fan, Changpin Li
Summary: This paper numerically studies the Allen-Cahn equations with different kinds of time fractional derivatives and investigates the influences of time derivatives on the solutions of the considered models.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Yuhang Zhu, Yinghao Zhao, Chaolin Song, Zeyu Wang
Summary: In this study, a novel approach called Time-Variant Reliability Updating (TVRU) is proposed, which integrates Kriging-based time-dependent reliability with parallel learning. This method enhances risk assessment in complex systems, showcasing exceptional efficiency and accuracy.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Chiara Cecilia Maiocchi, Valerio Lucarini, Andrey Gritsun, Yuzuru Sato
Summary: The predictability of weather and climate is influenced by the state-dependent nature of atmospheric systems. The presence of special atmospheric states, such as blockings, is associated with anomalous instability. Chaotic systems, like the attractor of the Lorenz '96 model, exhibit heterogeneity in their dynamical properties, including the number of unstable dimensions. The variability of unstable dimensions is linked to the presence of finite-time Lyapunov exponents that fluctuate around zero. These findings have implications for understanding the structural stability and behavior modeling of high-dimensional chaotic systems.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Christian Klein, Goksu Oruc
Summary: A numerical study on the fractional Camassa-Holm equations is conducted to construct smooth solitary waves and investigate their stability. The long-time behavior of solutions for general localized initial data from the Schwartz class of rapidly decreasing functions is also studied. Additionally, the appearance of dispersive shock waves is explored.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Vasily E. Tarasov
Summary: This paper extends the standard action principle and the first Noether theorem to consider the general form of nonlocality in time and describes dissipative and non-Lagrangian nonlinear systems. The general fractional calculus is used to handle a wide class of nonlocalities in time compared to the usual fractional calculus. The nonlocality is described by a pair of operator kernels belonging to the Luchko set. The non-holonomic variation equations of the Sedov type are used to describe the motion equations of a wide class of dissipative and non-Lagrangian systems. Additionally, the equations of motion are considered not only with general fractional derivatives but also with general fractional integrals. An application example is presented.
PHYSICA D-NONLINEAR PHENOMENA
(2024)