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Autor:
Hohloch, Sonja, Zadra, Federico
These lecture notes grew out of notes for courses around Integrable PDEs and the KdV equation given by the authors during the past five years at the University of Antwerp (Belgium). Comments and suggestions are welcome.
Comment: Lecture notes
Comment: Lecture notes
Externí odkaz:
http://arxiv.org/abs/2411.18504
Autor:
Balashov, O. S., Faminskii, A. V.
Direct and inverse initial-boundary problems on a bounded interval for systems of quasilinear evolution equations with general nonlinearities are considered. In the case of inverse problems conditions of integral overdetermination are introduced and
Externí odkaz:
http://arxiv.org/abs/2411.15810
Autor:
McConnell, Ryan, Oh, Seungly
We utilize a modulation restricted normal form approach to establish local well-posedness of the periodic Korteweg-de Vries equation in $H^s(\mathbb{T})$ for $s> -\frac23$. This work creates an analogue of the mKdV result by Nakanishi, Takaoka, and T
Externí odkaz:
http://arxiv.org/abs/2411.15069
Autor:
Titi, Edriss S., Victor, Collin
In this work, we study the applicability of the Azouani-Olson-Titi (AOT) nudging algorithm for continuous data assimilation to evolutionary dynamical systems that are not dissipative. Specifically, we apply the AOT algorithm to the Korteweg de-Vries
Externí odkaz:
http://arxiv.org/abs/2411.08273
Autor:
Robert, Tristan
In this work, we pursue our investigations on the Cauchy problem for a class of dispersive PDEs where a rough time coefficient is present in front of the dispersion. We show that if the PDE satisfies a strong non-resonance condition (Theorem 1.6), ev
Externí odkaz:
http://arxiv.org/abs/2410.23051
Autor:
Robert, Tristan
In this work, we study the Cauchy problem for a class of dispersive PDEs where a rough time coefficient is present in front of the dispersion. Under minimal assumptions on the occupation measure of this coefficient, we show that for the large class o
Externí odkaz:
http://arxiv.org/abs/2410.23038
We prove the asymptotic stability of the high speed solitary waves to the Benjamin equation. This is done by establishing a Liouville property for the nonlinear evolution of the Benjamin equation around these solitary waves. To do this, inspired by K
Externí odkaz:
http://arxiv.org/abs/2410.17846
Autor:
Curtin, Conor, Ivanov, Rossen
Publikováno v:
Wave Motion 129 (2024) 103343
The currents in the ocean have a serious impact on ocean dynamics, since they affect the transport of mass and thus the distribution of salinity, nutrients and pollutants. In many physically important situations the current depends quadratic-ally on
Externí odkaz:
http://arxiv.org/abs/2410.15209
We give a simpler proof for the local well-posedness of the modified Korteweg-de Vries equations and modified Benjamin-Ono equation in $H^{\frac{1}{4}}(\mathbb{R})$ and $H^{\frac{1}{2}}(\mathbb{R})$, respectively. The proof is based on the Strichartz
Externí odkaz:
http://arxiv.org/abs/2410.13656
We consider the Cauchy problem for the generalized fractional Korteweg-de Vries equation $$ u_t+D^\alpha u_x + u^p u_x= 0, \quad 1<\alpha\le 2, \quad p\in {\mathbb N}\setminus\{0\}, $$ with homogeneous initial data $\Phi$. We show that, under smallne
Externí odkaz:
http://arxiv.org/abs/2410.12063