Zobrazeno 1 - 10
of 355
pro vyhledávání: '"Lafortune, Stephane"'
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
In the present work we revisit the Painlev\'e property for partial differential equations. We consider the PDE variant of the relevant algorithm on the basis of the fundamental work of Weiss, Tabor and Carnevale and explore a number of relevant examp
Externí odkaz:
http://arxiv.org/abs/2404.00052
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:
Deng, Xijun, Lafortune, Stéphane
In this paper, we are concerned with a one-parameter family of peakon equations with cubic nonlinearity parametrized by a parameter usually denoted by the letter $b$. This family is called the ``$b$-Novikov'' since it reduces to the integrable Noviko
Externí odkaz:
http://arxiv.org/abs/2402.08759
We consider a diffusive Rosenzweig-MacArthur predator-prey model in the situation when the prey diffuses at the rate much smaller than that of the predator. In a certain parameter regime, the existence of fronts in the system is known: the underlying
Externí odkaz:
http://arxiv.org/abs/2401.15260
Autor:
Lafortune, Stéphane
The Novikov equation is a peakon equation with cubic nonlinearity which, like the Camassa-Holm and the Degasperis-Procesi, is completely integrable. In this article, we study the spectral and linear stability of peakon solutions of the Novikov equati
Externí odkaz:
http://arxiv.org/abs/2308.06655
A safety verification task involves verifying a system against a desired safety property under certain assumptions about the environment. However, these environmental assumptions may occasionally be violated due to modeling errors or faults. Ideally,
Externí odkaz:
http://arxiv.org/abs/2306.01025
Autor:
Deng, Xijun, Lafortune, Stéphane
Publikováno v:
In Journal of Differential Equations 15 January 2025 415:572-588
We derive the precise stability criterion for smooth solitary waves in the b-family of Camassa-Holm equations. The smooth solitary waves exist on the constant background. In the integrable cases b = 2 and b = 3, we show analytically that the stabilit
Externí odkaz:
http://arxiv.org/abs/2201.08094
Control systems should enforce a desired property for both expected modeled situations as well as unexpected unmodeled environmental situations. Existing methods focus on designing controllers to enforce the desired property only when the environment
Externí odkaz:
http://arxiv.org/abs/2110.04200