Zobrazeno 1 - 10
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pro vyhledávání: '"Perkins, Wesley R."'
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 prove that the modulational instability criterion of the formal Whitham modulation theory agrees with the spectral stability of long wavelength perturbations of periodic travelling wave solutions to the generalized Whitham equation. We use the sta
Externí odkaz:
http://arxiv.org/abs/2112.00049
Autor:
Johnson, Mathew A., Perkins, Wesley R.
We study the stability and nonlinear local dynamics of spectrally stable periodic wave trains of the Korteweg-de Vries / Kuramoto-Sivashinsky equation when subjected to classes of periodic perturbations. It is known that for each $N\in\mathbb{N}$, su
Externí odkaz:
http://arxiv.org/abs/2109.08459
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
Autor:
Johnson, Mathew A., Perkins, Wesley R.
We investigate the stability and nonlinear local dynamics of spectrally stable wave trains in reaction-diffusion systems. For each $N\in\mathbb{N}$, such $T$-periodic traveling waves are easily seen to be nonlinearly asymptotically stable (with asymp
Externí odkaz:
http://arxiv.org/abs/2009.12440
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
Autor:
Johnson, Mathew A., Perkins, Wesley R.
In this paper, we are interested in studying the modulational dynamics of interfacial waves rising buoyantly along a conduit of a viscous liquid. Formally, the behavior of modulated periodic waves on large space and time scales may be described throu
Externí odkaz:
http://arxiv.org/abs/1904.06348
Publikováno v:
Communications in Mathematical Physics; Oct2024, Vol. 405 Issue 10, p1-31, 31p
Autor:
Johnson, Mathew A., Perkins, Wesley R.
Publikováno v:
In Physica D: Nonlinear Phenomena August 2021 422
Publikováno v:
In Journal of Differential Equations 15 April 2021 280:315-354