Tootfinder

Investigation of shallow water waves near the coast or in lake environments via the KdV-Calogero-Bogoyavlenskii-Schiff equation
Peng-Fei Han, Yi Zhang
https://arxiv.org/abs/2404.18697 https://arxiv.org/pdf/2404.18697
arXiv:2404.18697v1 Announce Type: new
Abstract: Shallow water waves phenomena in nature attract the attention of scholars and play an important role in fields such as tsunamis, tidal waves, solitary waves, and hydraulic engineering. Hereby, for the shallow water waves phenomena in various natural environments, we study the KdV-Calogero-Bogoyavlenskii-Schiff (KdV-CBS) equation. Based on the Bell polynomial theory, the B{\"a}cklund transformation, Lax pair and infinite conservation laws of the KdV-CBS equation are derived, and it is proved that it is completely integrable in Lax pair sense. Various types of mixed solutions are constructed by using a combination of Homoclinic test method and Mathematica symbolic computations. These findings have important significance for the discipline, offering vital insights into the intricate dynamics of the KdV-CBS equation. We hope that our research results could help the researchers understand the nonlinear complex phenomena of the shallow water waves in oceans, rivers and coastal areas.

Nach Tod Nawalnys: USA plant Sanktionspaket gegen Russland
Als Reaktion auf den Tod des Oppositionsführers Nawalny bereitet das Weiße Haus nach eigenen Angaben weitere "umfangreiche Sanktionen" gegen Russland vor. Der Kommunikationsdirektor des Nationalen Sicherheitsrates, John Kirby, sagte am Dienstag, dass das neue Paket diesen Freitag vorgestellt werden soll.
Inwiefern die neuen Sanktionen bereits bestehende ergänzen werde…
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Ukraine-Liveblog: +++ Moskau verbietet US-Radiosender in Russland +++
Die US-Sendergruppe Radio Free Europe/Radio Liberty darf nach einem Verbot Moskaus nicht mehr in Russland senden. Landesweit demonstrieren polnische Bauern gegen die Einfuhr günstiger Agrarprodukte aus der Ukraine. Der Liveblog vom Dienstag zum Nachlesen.

This https://arxiv.org/abs/2308.09269 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Transition to anomalous dynamics in a simple random map
The famous Bernoulli shift (or dyadic transformation) is perhaps the simplest deterministic dynamical system exhibiting chaotic dynamics. It is a piecewise linear time-discrete map on the unit interval with a uniform slope larger than one, hence expanding, with a positive Lyapunov exponent and a uniform invariant density. If the slope is less than one the map becomes contracting, the Lyapunov exponent is negative, and the density trivially collapses onto a fixed point. Sampling from these two d…

Brain recordings in people before surgery reveal how all minds plan what to say before speaking https://nyulangone.org/news/brain-recordings-people-surgery-reveal-how-all-minds-plan-what-say-speaking "Latencies were…

Brain Recordings in People Before Surgery Reveal How All Minds Plan What to Say Before Speaking
An NYU Langone study of presurgical brain recordings shows that pauses in speech reveal information about how people’s brains plan what to say before speaking.

Kremlsprecher nennt Putins Ergebnis "außergewöhnlich" und attackiert Nawalnaja
Kreml-Sprecher Dmitri Peskow hat das Wahlergebnis Wladimir Putins bei der russischen Präsidentenwahl als "außergewöhnlich" bezeichnet. "Das ist ein absolut außergewöhnliches Ergebnis für den amtierenden Präsidenten (...) und eine deutliche Bestätigung der Unterstützung unserer Bevölkerung für ihren Staatschef", erklärte Peskow zu Putins Wahlergebnis…
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Ukraine-Liveblog: ++ Baerbock warnt vor "Gewaltsystem" Russlands ++
Bundesaußenministerin Baerbock hat dazu aufgerufen, dem "imperialen Wahn" des russischen Präsidenten Putin entgegenzutreten. Deutschland und Polen wollen bei der Lieferung von Munition an die Ukraine kooperieren. Der Liveblog vom Montag zum Nachlesen.

The Neumann-Moser dynamical system and the Korteweg-de Vries hierarchy
Polina Baron
https://arxiv.org/abs/2402.18079 https://arxiv.or…

The Neumann-Moser dynamical system and the Korteweg-de Vries hierarchy
At the focus of the paper are applications of the well-known Moser transformation of the C. Neumann dynamical system. It yields us a new quadratic integrable dynamical system on $\mathbb{C}^{3n+1}$, which we call the Neumann-Moser dynamical system. We present an explicit formula of the inverse of the Moser transformation. Consequently, we obtain explicitly an invertible transformation of the Uhlenbeck-Devaney integrals of the Neumann system into the integrals of our system. One of the main resu…

Deformed cluster maps of type $A_{2N}$
Jan E. Grabowski, Andrew N. W. Hone, Wookyung Kim
https://arxiv.org/abs/2402.18310 https://arx…

Deformed cluster maps of type $A_{2N}$
We extend recent work of the third author and Kouloukas by constructing deformations of integrable cluster maps corresponding to the Dynkin types $A_{2N}$, lifting these to higher-dimensional maps possessing the Laurent property and demonstrating integrality of the deformations for $N\leq 3$. This provides the first infinite class of examples (in arbitrarily high rank) of such maps and gives information on the associated discrete integrable systems. Key to our approach is a ``local expansion'' …

This https://arxiv.org/abs/2312.00524 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Caputo Fractional Standard Map: Scaling Invariance Analyses
In this paper, we investigate the scaling invariance of survival probability in the Caputo fractional standard map of the order $1<α<2$ considered on a cylinder. We consider relatively large values of the nonlinearity parameter $K$ for which the map is chaotic. The survival probability has a short plateau followed by an exponential decay and is scaling invariant for all considered values of $α$ and $K$.

Analytical and numerical studies for integrable and non-integrable fractional discrete modified Korteweg-de Vries hierarchies
Qin-Ling Liu, Rui Guo, Ya-Hui Huang, Xin Li
https://arxiv.org/abs/2402.13872

Analytical and numerical studies for integrable and non-integrable fractional discrete modified Korteweg-de Vries hierarchies
Under investigation in this paper is the fractional integrable and non-integrable discrete modified Korteweg-de Vries hierarchies. The linear dispersion relations, completeness relations, inverse scattering transform, and fractional soliton solutions of the fractional integrable discrete modified Korteweg-de Vries hierarchy will be explored. The inverse scattering problem will be solved accurately by using Gel'fand-Levitan-Marchenko (GLM) equations and Riemann-Hilbert (RH) problem. The peak vel…

This https://arxiv.org/abs/2310.19584 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Integrable maps in 4D and modified Volterra lattices
In recent work, we presented the construction of a family of difference equations associated with the Stieltjes continued fraction expansion of a certain function on a hyperelliptic curve of genus $g$. As well as proving that each such discrete system is an integrable map in the Liouville sense, we also showed it to be an algebraic completely integrable system. In the discrete setting, the latter means that the generic level set of the invariants is an affine part of an abelian variety, in this…