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pro vyhledávání: '"Johnson, Mathew A."'
Autor:
Johnson, Mathew A., Oregero, Jeffrey
In this paper, we study the nonlinear wave modulation of arbitrary amplitude periodic traveling wave solutions of the Camassa-Holm (CH) equation. Slow modulations of wave trains is often described through Whitham's theory of modulations, which at lea
Externí odkaz:
http://arxiv.org/abs/2410.22219
We study the spectral stability of smooth, small-amplitude periodic traveling wave solutions of the Novikov equation, which is a Camassa-Holm type equation with cubic nonlinearities. Specifically, we investigate the $L^2(\mathbb{R})$-spectrum of the
Externí odkaz:
http://arxiv.org/abs/2409.13969
We study the orbital stability of smooth solitary wave solutions of the Novikov equation, which is a Camassa-Holm type equation with cubic nonlinearities. These solitary waves are shown to exist as a one-parameter family (up to spatial translations)
Externí odkaz:
http://arxiv.org/abs/2403.10685
Autor:
Ehrman, Brett, Johnson, Mathew A.
In this paper, we identify criteria that guarantees the nonlinear orbital stability of a given periodic traveling wave solution within the b-family Camassa-Holm equation. These periodic waves exist as 3-parameter families (up to spatial translations)
Externí odkaz:
http://arxiv.org/abs/2309.17289
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 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 of the ori
Externí odkaz:
http://arxiv.org/abs/2305.08128
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:
Ehrman, Brett, Johnson, Mathew A.
Publikováno v:
In Physica D: Nonlinear Phenomena May 2024 461
Using a nonlocal version of the center manifold theorem and a normal form reduction, we prove the existence of small-amplitude generalized solitary-wave solutions and modulated solitary-wave solutions to the steady gravity-capillary Whitham equation
Externí odkaz:
http://arxiv.org/abs/2103.02675