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Related papers: Breather solutions for semilinear wave equations

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Existence of large-amplitude time-periodic breathers localized near a single site is proved for the discrete Klein--Gordon equation, in the case when the derivative of the on-site potential has a compact support. Breathers are obtained at…

Pattern Formation and Solitons · Physics 2010-11-30 Guillaume James , Dmitry Pelinovsky

We construct series solutions to all orders for breathers of Klein-Gordon equations, in powers of an amplitude parameter epsilon, under a sign condition on the coefficients of the expansion of the nonlinearity. All terms may be computed…

Analysis of PDEs · Mathematics 2017-09-25 Satyanad Kichenassamy

We derive a Hamiltonian version of the ${\cal PT}$-symmetric discrete nonlinear Schr\"{o}dinger equation that describes synchronized dynamics of coupled pendula driven by a periodic movement of their common strings. In the limit of weak…

Mathematical Physics · Physics 2016-05-23 Alexander Chernyavsky , Dmitry E. Pelinovsky

This paper is devoted to the study of periodic solutions for a semilinear Euler-Bernoulli beam equation with variable coefficients. Such mathematical model may be described the infinitesimal, free, undamped in-plane bending vibrations of a…

Dynamical Systems · Mathematics 2021-03-17 Hui Wei , Shuguan Ji

We demonstrate that stabilization of solitons of the multidimensional Schrodinger equation with a cubic nonlinearity may be achieved by a suitable periodic control of the nonlinear term. The effect of this control is to stabilize the…

Pattern Formation and Solitons · Physics 2009-11-10 Gaspar D. Montesinos , Victor M. Perez-Garcia , Pedro Torres

We are concerned with numerical approximations of breather solutions for the cubic Whitham equation which arises as a water-wave model for interfacial waves. The model combines strong nonlinearity with the non-local character of the…

Pattern Formation and Solitons · Physics 2022-02-15 Henrik Kalisch , Miguel A. Alejo , Adán J. Corcho , Didier Pilod

Breather solutions of the nonlinear Schr\"{o}dinger equation are derived in this paper: the Soliton on Finite Background, the Ma breather and the rational breather. A special Ansatz of a displaced phase-amplitude equation with respect to a…

Fluid Dynamics · Physics 2011-10-25 N. Karjanto , E. van Groesen

We discuss the existence of breathers and lower bounds on their power, in nonlinear Schr\"odinger lattices with nonlinear hopping. Our methods extend from a simple variational approach to fixed point arguments, deriving lower bounds for the…

Pattern Formation and Solitons · Physics 2015-05-20 N. I. Karachalios , B. Sánchez-Rey , P. G. Kevrekidis , J. Cuevas

We prove the existence and the linear stability of small amplitude time {\it quasi-periodic} standing wave solutions (i.e. periodic and even in the space variable $ x $) of a $ 2 $-dimensional ocean with infinite depth under the action of…

Analysis of PDEs · Mathematics 2018-04-13 Massimiliano Berti , Riccardo Montalto

Exact solutions for the generalized nonlinear Schr\"odinger (NLS) equation with inhomogeneous complex linear and nonlinear potentials are found. We have found localized and periodic solutions for a wide class of localized and periodic…

Pattern Formation and Solitons · Physics 2015-05-20 F. Kh. Abdullaev , V. V. Konotop , M. Salerno , A. V. Yulin

We consider the periodic solutions of a semilinear variable coefficient wave equation arising from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. The variable coefficient…

Analysis of PDEs · Mathematics 2021-08-24 Hui Wei , Shuguan Ji

In this work we derive some blow-up results for semilinear wave equations both in de Sitter and anti-de Sitter spacetimes. By requiring suitable conditions on a time-dependent factor in the nonlinear term, we prove the blow-up in finite…

Analysis of PDEs · Mathematics 2022-06-22 Alessandro Palmieri , Hiroyuki Takamura

In this work, a rigorous proof of the nonexistence of breather solutions for NLS equations is presented. By using suitable virial functionals, we are able to characterize the nonexistence of breather solutions, different from standing…

Analysis of PDEs · Mathematics 2025-01-09 Miguel Á. Alejo , Adán J. Corcho

This work focuses on the study of time-periodic solutions, including breathers, in a nonlinear lattice consisting of elements whose contacts alternate between strain-hardening and strain-softening. The existence, stability, and bifurcation…

Pattern Formation and Solitons · Physics 2023-05-24 Marisa M. Lee , Efstathios G. Charalampidis , Siyuan Xing , Christopher Chong , Panayotis G. Kevrekidis

In this paper our first aim is to identify a large class of non-linear functions $\,f(\cdot)\,$ for which the IVP for the generalized Korteweg-de Vries equation does not have breathers or "small" breathers solutions. Also we prove that all…

Analysis of PDEs · Mathematics 2018-08-15 Claudio Muñoz , Gustavo Ponce

The global existence for semilinear wave equations with space-dependent critical damping $\partial_t^2u-\Delta u+\frac{V_0}{|x|}\partial_t u=f(u)$ in an exterior domain is dealt with, where $f(u)=|u|^{p-1}u$ and $f(u)=|u|^p$ are in mind.…

Analysis of PDEs · Mathematics 2021-06-14 Motohiro Sobajima

We consider damped and forced discrete nonlinear Schr\"odinger equations on the lattice $\mathbb{Z}$. First we establish the existence of periodic and quasiperiodic breather solutions for periodic and quasiperiodic driving, respectively.…

Mathematical Physics · Physics 2023-04-19 Dirk Hennig

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

We consider the discrete p-Schr\"odinger (DpS) equation, which approximates small amplitude oscillations in chains of oscillators with fully-nonlinear nearest-neighbors interactions of order alpha = p-1 >1. Using a mapping approach, we…

Pattern Formation and Solitons · Physics 2013-12-18 Guillaume James , Yuli Starosvetsky

In this paper we give a systematic and simple account that put in evidence that many breather solutions of integrable equations satisfy suitable variational elliptic equations, which also implies that the stability problem reduces in some…

Mathematical Physics · Physics 2016-04-29 Miguel A. Alejo , Claudio Muñoz , José M. Palacios