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In this paper the coupled Maxwell-Bloch equations which describe the propagation of two optical pulses in an optical medium with coherent three-level atoms are studied by Darboux transformation. The general nth-order rogue wave solution…

Exactly Solvable and Integrable Systems · Physics 2020-02-12 Xin Wang , Lei Wang , Chong Liu

We study spatial optical solitons in a one-dimensional nonlinear photonic crystal created by an array of thin-film nonlinear waveguides, the so-called Dirac-comb nonlinear lattice. We analyze modulational instability of the extended…

Pattern Formation and Solitons · Physics 2007-05-23 Andrey A. Sukhorukov , Yuri S. Kivshar

We study the propagation of solitary waves in a Fermi-Pasta-Ulam-Tsingou (FPUT) lattice with small random heterogeneity in the linear spring force. Perturbed by the random environment, solitary waves lose energy through a radiative tail,…

Dynamical Systems · Mathematics 2025-09-25 Hermen Jan Hupkes , Joshua A. McGinnis , Rik W. S. Westdorp , J. Douglas Wright

It is the aim of the paper to present a new point of view on rotational elasticity in a nonlinear setting using orthogonal matrices. The proposed model, in the linear approximation, can be compared to the well known equilibrium equations of…

Mathematical Physics · Physics 2015-10-09 Christian G. Boehmer , Nicola Tamanini

We show existence of solitary-wave solutions to the equation \begin{equation*} u_t+ (Lu - n(u))_x = 0\,, \end{equation*} for weak assumptions on the dispersion $L$ and the nonlinearity $n$. The symbol $m$ of the Fourier multiplier $L$ is…

Analysis of PDEs · Mathematics 2020-03-16 Ola Maehlen

In this paper, we employ a combination of analytical and numerical techniques to investigate the dynamics of lattice envelope vector soliton solutions propagating within a one-dimensional chain of flexible mechanical metamaterial. To model…

Pattern Formation and Solitons · Physics 2024-06-17 Antoine Demiquel , Vassos Achilleos , Georgios Theocharis , Vincent Tournat

Modulation instability in a nonlinear optical waveguide array with alternating positive and negative refractive indices is investigated analytically. Particular solutions of a system of coupled nonlinear equations are found. These solutions…

Pattern Formation and Solitons · Physics 2014-09-30 A. A. Dovgiy , A. I. Maimistov

We consider a bimodal light field envelope propagating in a bulk medium characterized by competing cubic and quintic nonlinearities. The subfields are coupled by a cross-phase modulation term and experience effective attraction. We find…

Optics · Physics 2026-01-05 Dmitry A. Zezyulin

The solitary wave solution and periodic solutions expressed in terms of elliptic Jacobi's functions are obtained for the nonlinear Schr\"{o}dinger equation governing the propagation of pulses in optical fibers including the effects of…

Pattern Formation and Solitons · Physics 2020-04-22 Vladimir I. Kruglov

A numerical fluid simulation investigation of the temporal evolution of a special class of traveling wave solution of the one dimensional relativistic cold plasma model is reported.The solutions consist of coupled electromagnetic and plasma…

Plasma Physics · Physics 2009-11-11 Vikrant Saxena , Amita Das , Abhijit Sen , Predhiman Kaw

Roughly speaking a solitary wave is a solution of a field equation whose energy travels as a localised packet and which preserves this localisation in time. A soliton is a solitary wave which exhibits some strong form of stability so that…

Analysis of PDEs · Mathematics 2008-10-29 J. Bellazzini , V. Benci , C. Bonanno , E. Sinibaldi

Light propagation in optical waveguides with periodically modulated index of refraction and alternating gain and loss are investigated for linear and nonlinear systems. Based on a multiscale perturbation analysis, it is shown that for many…

Optics · Physics 2015-06-23 Sean Nixon , Jianke Yang

We reveal and observe experimentally significant modifications undertaken by discrete solitons in waveguide lattices upon the continuous transformation of the lattice structure from one-dimensional to two-dimensional. Light evolution and…

Rogue waves are solitary waves with extreme amplitudes, which appear to be a ubiquitous phenomenon in nonlinear wave propagation, with the requirement for a nonlinearity being their only unifying characteristics. While many mechanisms have…

The propagation of localized edge modes in photonic honeycomb lattices, formed from an array of adiabatically varying periodic helical waveguides, is considered. Asymptotic analysis leads to an explicit description of the underlying…

Optics · Physics 2014-11-25 M. J. Ablowitz , C. W. Curtis , Y. -P. Ma

The dynamics of solitary gravity-capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time dependent solutions, we simplify the full potential…

Fluid Dynamics · Physics 2015-06-05 Zhan Wang , Paul A Milewski

We study waves in a chain of dispersively coupled phase oscillators. Two approaches -- a quasi-continuous approximation and an iterative numerical solution of the lattice equation -- allow us to characterize different types of traveling…

Pattern Formation and Solitons · Physics 2011-10-17 Karsten Ahnert , Arkardy Pikovsky

We consider a two-dimensional nonlinear waveguide with distributed gain and losses. The optical potential describing the system consists of an unperturbed complex potential depending only on one transverse coordinate, i.e., corresponding to…

We consider the full set of Maxwell equations in a slab or cylindrical waveguide with a cubically nonlinear material law for the polarization of the electric field. The nonlinear polarization may be instantaneous or retarded, and we assume…

Analysis of PDEs · Mathematics 2024-07-29 Sebastian Ohrem , Wolfgang Reichel

This paper investigates solitary water waves propagating along the surface of a two-dimensional dielectric fluid with constant vorticity in the presence of an external electric field. We formulate the system as a nonlinear free boundary…

Analysis of PDEs · Mathematics 2026-04-28 Tingting Feng , Yong Zhang , Zhitao Zhang