Zobrazeno 1 - 10
of 131
pro vyhledávání: '"Haragus, Mariana"'
We study the nonlinear dynamics of perturbed, spectrally stable $T$-periodic stationary solutions of the Lugiato-Lefever equation (LLE), a damped nonlinear Schr\"odinger equation with forcing that arises in nonlinear optics. It is known that for each
Externí odkaz:
http://arxiv.org/abs/2307.01176
We study the transverse dynamics of two-dimensional traveling periodic waves for the gravity--capillary water-wave problem. The governing equations are the Euler equations for the irrotational flow of an inviscid fluid layer with free surface under t
Externí odkaz:
http://arxiv.org/abs/2203.14848
Autor:
Haragus, Mariana, Pelinovsky, Dmitry
Relying upon tools from the theory of integrable systems, we discuss the linear instability of the Kuznetsov-Ma breathers and the Akhmediev breathers of the focusing nonlinear Schr{\"o}dinger equation. We use the Darboux transformation to construct s
Externí odkaz:
http://arxiv.org/abs/2112.14426
Using a variational method, we prove the existence of heteroclinic solutions for a 6dimensional system of ordinary differential equations. We derive this system from the classical B{\'e}nard-Rayleigh problem near the convective instability threshold.
Externí odkaz:
http://arxiv.org/abs/2112.10546
We consider the nonlinear stability of spectrally stable periodic waves in the Lugiato-Lefever equation (LLE), a damped nonlinear Schr\"odinger equation with forcing that arises in nonlinear optics. So far, nonlinear stability of such solutions has o
Externí odkaz:
http://arxiv.org/abs/2106.01910
We study the linear dynamics of spectrally stable $T$-periodic stationary solutions of the Lugiato-Lefever equation (LLE), a damped nonlinear Schr\"odinger equation with forcing that arises in nonlinear optics. Such $T$-periodic solutions are nonline
Externí odkaz:
http://arxiv.org/abs/2007.03499
Publikováno v:
In Journal of Differential Equations 15 May 2023 355:193-218
Publikováno v:
Communications in Mathematical Physics; Oct2024, Vol. 405 Issue 10, p1-31, 31p
We present a general counting result for the unstable eigenvalues of linear operators of the form $JL$ in which $J$ and $L$ are skew- and self-adjoint operators, respectively. Assuming that there exists a self-adjoint operator $K$ such that the opera
Externí odkaz:
http://arxiv.org/abs/1609.05125
Autor:
Haragus, Mariana, Wahlén, Erik
Publikováno v:
J. Differential Equations 262 (2017) 3235-3249
We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic waves at
Externí odkaz:
http://arxiv.org/abs/1604.00288