English
Related papers

Related papers: Travelling waves in nonlinear magneto-inductive la…

200 papers

The present paper is concerned with the existence of traveling wave solutions of the asymptotic model, derived by the authors in a previous work, to approximate the unidirectional evolution of a collision-free plasma in a magnetic field.…

Analysis of PDEs · Mathematics 2024-10-14 Diego Alonso-Orán , Angel Durán , Rafael Granero-Belinchón

Metamaterials can enable peculiar static and dynamic behavior (such as negative effective mass density, dynamical stiffness, and Poisson's ratio) due to their geometry rather than their chemical composition. The geometry of these…

Soft Condensed Matter · Physics 2022-01-03 Audrey A. Watkins , Austin Eichelberg , Osama R. Bilal

Vector solitary waves are nonlinear waves of coupled polarizations that propagate with constant velocity and shape. In mechanics, they hold the potential to control locomotion, mitigate shocks and transfer information, among other…

Soft Condensed Matter · Physics 2020-06-23 Ron Ziv , Gal Shmuel

We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…

Analysis of PDEs · Mathematics 2014-10-28 A. Hoffman , H. J. Hupkes , E. Van Vleck

A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the…

Pattern Formation and Solitons · Physics 2013-12-17 David I. Ketcheson , Manuel Quezada de Luna

We study the existence and stability of periodic traveling-wave solutions for the quadratic and cubic nonlinear Schr\"odinger equations in one space dimension.

Exactly Solvable and Integrable Systems · Physics 2011-12-20 Sevdzhan Hakkaev , Iliya D. Iliev , Kiril Kirchev

In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as Mass-in-Mass systems. We use 3 distinct approaches to identify relevant traveling waves. The first consists of…

Pattern Formation and Solitons · Physics 2015-06-23 H. Xu , P. G. Kevrekidis , A. Stefanov

This paper is devoted to the study of traveling waves for monotone evolution systems of bistable type. Under an abstract setting, we establish the existence of bistable traveling waves for discrete and continuous-time monotone semiflows.…

Analysis of PDEs · Mathematics 2011-02-23 Jian Fang , Xiao-Qiang Zhao

Presented is a data-driven Machine Learning (ML) framework for the identification and modeling of traveling wave spatiotemporal dynamics. The presented framework is based on the steadily-propagating traveling wave ansatz, $u(x,t) = U(\xi=x…

Fluid Dynamics · Physics 2021-05-05 James Koch

The present paper deals with sufficient conditions for orbital stability of periodic waves of a general class of evolution equations supporting nonlinear dispersive waves. Our method can be seen as an extension to spatially periodic waves…

Analysis of PDEs · Mathematics 2016-11-16 Giovana Alves , Fábio Natali , Ademir Pastor

We prove the existence of periodic travelling wave solutions for general discrete nonlinear Klein-Gordon systems, considering both cases of hard and soft on-site potentials. In the case of hard on-site potentials we implement a fixed point…

Analysis of PDEs · Mathematics 2023-07-21 Dirk Hennig , Nikos I. Karachalios

This work presents a mechanism by which non-reciprocal wave transmission is achieved in a class of gyric metamaterial lattices with embedded rotating elements. A modulation of the device's angular momentum is obtained via prescribed…

Applied Physics · Physics 2020-08-12 M. A. Attarzadeh , S. Maleki , J. L. Crassidis , M. Nouh

We introduce and study a family of lattice equations which may be viewed either as a strongly nonlinear discrete extension of the Gardner equation, or a non-convex variant of the Lotka-Volterra chain. Their deceptively simple form supports…

Pattern Formation and Solitons · Physics 2021-08-11 Philip Rosenau , Arkady Pikovsky

We consider a 2+1 dimensional wave equation appearing in the context of polarized waves for the nonlinear Maxwell equations. The equation is quasilinear in the time derivatives and involves two material functions $V$ and $\Gamma$. We prove…

Analysis of PDEs · Mathematics 2022-04-13 Gabriele Bruell , Piotr Idzik , Wolfgang Reichel

We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…

Pattern Formation and Solitons · Physics 2015-06-26 Robert L. Pego , Jose Raul Quintero

Traveling waves triggered by a phase slip in coupled map lattices are studied. A local phase slip affects globally the system, which is in strong contrast with kink propagation. Attractors with different velocities coexist, and form…

chao-dyn · Physics 2009-10-22 Kunihiko Kaneko

In this note, we study the existence of traveling waves of a surface model in a non-newtonian fluid with odd viscosity. The proof relies on nonlinear bifurcation techniques.

Analysis of PDEs · Mathematics 2024-07-30 Diego Alonso-Orán , Claudia García , Rafael Granero-Belinchón

In this paper we study the dynamics of metamaterials composed of high-contrast subwavelength resonators and show the existence of localised modes in such a setting. A crucial assumption in this paper is time-modulated material parameters.…

Analysis of PDEs · Mathematics 2025-01-13 Habib Ammari , Erik Orvehed Hiltunen , Liora Rueff

A key feature of $(1+1)$-dimensional nonlinear wave equations is that they admit left or right traveling waves, under appropriate algebraic conditions on the nonlinearities. In this paper, we prove global stability of such traveling wave…

Analysis of PDEs · Mathematics 2023-01-31 Louis Dongbing Cha , Arick Shao

We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are…

Exactly Solvable and Integrable Systems · Physics 2009-11-10 P. G. Kevrekidis , S. V. Dmitriev , S. Takeno , A. R. Bishop , E. C. Aifantis