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The well-known Stokes waves refer to periodic traveling waves under the gravity at the free surface of a two dimensional full water wave system. In this paper, we prove that small-amplitude Stokes waves with infinite depth are nonlinearly…

Analysis of PDEs · Mathematics 2021-01-01 Gong Chen , Qingtang Su

We study the modulational instability of small-amplitude periodic traveling wave solutions in a dispersion generalized Ostrovsky equation. Specifically, we investigate the invertibility of the associated linearized operator in the vicinity…

Analysis of PDEs · Mathematics 2024-09-25 Bhavna , Mathew A. Johnson , Ashish Kumar Pandey

The unexpected emerging stability of a time-modulated magnetic guide, realized without external offset fields, is demonstrated. We found a steady periodic solution around which the nonlinear dynamics is linearized. To investigate the…

Quantum Physics · Physics 2019-12-17 Carlos L. Garrido Alzar

We develop a full theoretical analysis of the nonlinear interactions of the two polarizations of a waveguide by means of a vectorial model of pulse propagation which applies to high index subwavelength waveguides. In such waveguides there…

Optics · Physics 2015-06-04 Shahraam Afshar V. , M. A. Lohe , Wen Qi Zhang , Tanya M. Monro

We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we…

Optics · Physics 2016-08-24 S. Randoux , P. Walczak , M. Onorato , P. Suret

In this work we derive evolution equations for the nonlinear behavior of a coasting beam under the influence of a resonator impedance. Using a renormalization group approach we find a set of coupled nonlinear equations for the beam density…

Accelerator Physics · Physics 2007-05-23 S. I. Tzenov , P. L. Colestock

We study the evolution of an inverted spin ensemble coupled to a cavity. The inversion itself presents an inherent instability of the system; however, the inhomogeneous broadening of spin-resonance frequencies presents a stabilizing…

Quantum Physics · Physics 2015-06-11 Brian Julsgaard , Klaus Mølmer

Inhomogeneous plasmas filaments instabilities are investigated by using the techniques of classical differential geometry of curves where Frenet torsion and curvature describe completely the motion of curves. In our case the Frenet frame…

Mathematical Physics · Physics 2007-05-23 Garcia de Andrade

We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…

Pattern Formation and Solitons · Physics 2009-11-07 Roman O. Grigoriev , Andreas Handel

We investigate the nonlinear interaction between two laser beams in a plasma in the weakly nonlinear and relativistic regime. The evolution of the laser beams is governed by two nonlinear Schroedinger equations that are coupled with the…

Plasma Physics · Physics 2007-05-23 P. K. Shukla , B. Eliasson , M. Marklund , L. Stenflo , I. Kourakis , M. Parviainen , M. E. Dieckmann

This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic…

Quantum Physics · Physics 2013-03-26 Ian R. Petersen

The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic…

Pattern Formation and Solitons · Physics 2016-10-18 Noé Jiménez , Ahmed Mehrem , Rubén Picó , Lluís M. García-Raffi , Víctor J. Sánchez-Morcillo

Nonlinear dynamics of the electron-cyclotron instability driven by the electron $\mathbf{E\times B}$ current in crossed electric and magnetic field is studied. In nonlinear regime the instability proceeds by developing a large amplitude…

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity…

Pattern Formation and Solitons · Physics 2009-11-07 J. F. Corney , Ole Bang

The modulational instability in the class of NLS equations is discussed using a statistical approach. A kinetic equation for the two-point correlation function is studied in a linear approximation, and an integral stability equation is…

Exactly Solvable and Integrable Systems · Physics 2009-11-11 A. T. Grecu , D. Grecu , Anca Visinescu

The paper deals with a nonlinear evolution equation describing the dynamics of a non homogeneous multiply hinged beam, subject to a nonlocal restoring force of displacement type. First, a spectral analysis for the associated weighted…

Analysis of PDEs · Mathematics 2020-10-21 E. Berchio , A. Falocchi , M. Garrione

We study the plane (not necessarily monochromatic) gravitational waves at nonlinear quadratic order on a flat background in vacuum. We show that, in the harmonic gauge, the nonlinear waves are unstable. We argue that, at this order, this…

General Relativity and Quantum Cosmology · Physics 2017-07-10 Fabio Briscese , Paolo Maria Santini

The amplitude equation for an unstable electrostatic wave is analyzed using an expansion in the mode amplitude $A(t)$. In the limit of weak instability, i.e. $\gamma\to 0^+$ where $\gamma$ is the linear growth rate, the nonlinear…

patt-sol · Physics 2009-10-30 John David Crawford , Anandhan Jayaraman

Nonlinear self-modulation of the dust acoustic waves is studied, in the presence of non-thermal (non-Maxwellian) ion and electron populations. By employing a multiple scale technique, a nonlinear Schrodinger-type equation (NLSE) is derived…

Plasma Physics · Physics 2015-06-26 Ioannis Kourakis , P. K. Shukla

We introduce a one-dimensional model based on the nonlinear Schrodinger/Gross-Pitaevskii equation where the local nonlinearity is subject to spatially periodic modulation in terms of the Jacobi dn function, with three free parameters…

Pattern Formation and Solitons · Physics 2018-01-17 E. Ding , H. N. Chan , K. W. Chow , K. Nakkeeran , B. A. Malomed