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Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…

Plasma Physics · Physics 2023-05-30 Stephan I. Tzenov , Klaus M. Spohr , Kazuo A. Tanaka

Waves with different symmetries exist in two-component Bose-Einstein condensates (BECs) whose dynamics is described by a system of coupled Gross-Pitaevskii (GP) equations. A first type of waves corresponds to excitations for which the…

Quantum Gases · Physics 2016-12-22 A. M. Kamchatnov , Y. V. Kartashov , P. -É. Larré , N. Pavloff

We derive the two-breather solution of the class I infinitely extended nonlinear Schrodinger equation (NLSE). We present a general form of this multi-parameter solution that includes infinitely many free parameters of the equation and free…

Exactly Solvable and Integrable Systems · Physics 2020-09-22 Matthew Crabb , Nail Akhmediev

Breathers have been experimentally and theoretically found in many physical systems -- in particular, in integrable nonlinear-wave models. A relevant problem is to study the \textit{breather gas}, which is the limit, for $N\rightarrow…

Exactly Solvable and Integrable Systems · Physics 2025-10-17 Weifang Weng , Guoqiang Zhang , Boris A. Malomed , Zhenya Yan

Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are approximated by equations of the discrete nonlinear Schrodinger type. We show how to justify this approximation by two methods, which have been very popular in the…

Dynamical Systems · Mathematics 2016-09-21 D. Pelinovsky , T. Penati , S. Paleari

The purpose of this paper is to construct small-amplitude breather solutions for a nonlinear Klein-Gordon equation posed on a periodic metric graph via spatial dynamics and center manifold reduction. The major difficulty occurs from the…

Analysis of PDEs · Mathematics 2018-12-06 Daniela Maier

We consider the evolution of narrow-band wave trains of finite amplitude in a nonlinear dispersive system which is described by the Klein--Gordon equation with arbitrary polynomial nonlinearity. We use a new perturbative technique which…

Pattern Formation and Solitons · Physics 2015-01-28 V. P. Lukomsky , I. S. Gandzha

This is a continuation of Ref.[1](arXiv:nlin.PS/2001.07758v1). In the present paper, we consider the solution to the modified Benjamin-Bona-Mahony equation $u_{ t} + C u_{z} + \beta u_{zzt} + a u^{2} u_{z}=0$ using the generalized…

Exactly Solvable and Integrable Systems · Physics 2020-05-22 G. T. Adamashvili

This paper is concerned with breather solutions of a radially symmetric curl-curl wave equation with double power nonlinearity. By considering the solutions with a special form, we obtain a family of ordinary differential equations (ODEs)…

Analysis of PDEs · Mathematics 2024-03-13 Xin Meng , Shuguan Ji

Solitons and breathers are localized solutions of integrable systems that can be viewed as "particles'' of complex statistical objects called soliton and breather gases. In view of the growing evidence of their ubiquity in fluids and…

Pattern Formation and Solitons · Physics 2020-05-13 Gennady El , Alexander Tovbis

In numerical experiments involving nonlinear solitary waves propagating through nonhomogeneous media one observes "breathing" in the sense of the amplitude of the wave going up and down on a much faster scale than the motion of the wave. In…

Analysis of PDEs · Mathematics 2015-05-13 Justin Holmer , Maciej Zworski

We consider a quasi-one-dimensional two-component Bose-Einstein condensate subject to a coherent coupling between its components, such as realized in spin-orbit coupled condensates. We study how nonlinearity modifies the dynamics of the…

Quantum Gases · Physics 2016-04-20 T. Congy , A. Kamchatnov , N. Pavloff

Using the Darboux transformation for the Korteweg-de Vries equation, we construct and analyze exact solutions describing the interaction of a solitary wave and a traveling cnoidal wave. Due to their unsteady, wavepacket-like character,…

Pattern Formation and Solitons · Physics 2023-04-26 Mark A. Hoefer , Ana Mucalica , Dmitry E. Pelinovsky

In this paper we investigate the emergence of time-periodic and and time-quasiperiodic (sometimes infinitely long lived and sometimes very long lived or metastable) solutions of discrete nonlinear wave equations: discrete sine Gordon,…

Pattern Formation and Solitons · Physics 2007-05-23 P. G. Kevrekidis , M. I. Weinstein

We construct small amplitude breathers in 1D and 2D Klein--Gordon infinite lattices. We also show that the breathers are well approximated by the ground state of the nonlinear Schroedinger equation. The result is obtained by exploiting the…

Dynamical Systems · Mathematics 2013-10-09 D. Bambusi , S. Paleari , T. Penati

We present a one-line closed form expression for the three-parameter breather of the nonlinear Schr\"odinger equation. This provides an analytic proof of the time period doubling observed in experiments. The experimental check that some…

Pattern Formation and Solitons · Physics 2021-04-14 Robert Conte , ENS Paris-Saclay

In this review, a more general theory of self-induced transparency (SIT) in comparison with the theory of McCall and Hahn is considered. Using the recently developed generalized perturbative reduction method (GPRM) the SIT equations are…

Mesoscale and Nanoscale Physics · Physics 2026-01-28 G. T. Adamashvili

In the present work, we study the nonlinear dynamics of a microtubule, an important part of the cytoskeleton. We use a two-component model of the relevant system. A crucial nonlinear differential equation is solved with semi-discrete…

We construct breather and rogue wave solutions of a variable coefficient nonlinear Schr\"odinger equation with an external linear potential. This generalized model describes the nonlinear wave propagation in an inhomogeneous plasma/medium.…

Exactly Solvable and Integrable Systems · Physics 2014-07-14 K. Manikandan , M. Senthilvelan

To study the propagation of nonlinear waves across Y- and T-type junctions, we consider the 2D sine--Gordon equation as a model and study the dynamics of kinks and breathers in such geometries. The comparison of the energies reveals that…

Pattern Formation and Solitons · Physics 2020-03-24 Jean-Guy Caputo , Denys Dutykh