Tootfinder

A State of the Art on Recent Progress and Emerging Challenges on Energy Transfer Between Vibrating Modes Under an External Mechanical Force With Time-Varying Frequency From 2020 to 2025
Jose Manoel Balthazar, Jorge Luis Palacios Felix, Mauricio A. Ribeiro, Angelo Marcelo Tusset, Jeferson Jose de Lima, Vinicius Piccirillo, Julijana Simonovic, Nikola D. Nevsic, Marcos Varanis, Clivaldo de Oliveira, Raphaela C. Machado, Gabriella O M Oliveira

A State of the Art on Recent Progress and Emerging Challenges on Energy Transfer Between Vibrating Modes Under an External Mechanical Force With Time-Varying Frequency From 2020 to 2025
In this paper, we discuss an example of current importance with a future perspective in engineering, in which excitation sources always have limited power, limited inertia, and their frequencies vary according to the instantaneous state of the vibrating system. Practical examples of non-ideal systems are considered. The most common phenomenon for this kind of system is discussed. The period considered is from 2020 to 2025. The specific properties of various models are also discussed. Directions…

This https://arxiv.org/abs/2505.09918 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Classical integrable spin chains of Landau-Lifshitz type from R-matrix identities
We describe a family of 1+1 classical integrable space-discrete models of the Landau-Lifshitz type through the usage of ansatz for $U$-$V$ (Lax) pair with spectral parameter satisfying the semi-discrete Zakharov-Shabat equation. The ansatz for $U$-$V$ pair is based on $R$-matrices satisfying the associative Yang-Baxter equation and certain additional properties. Equations of motion are obtained using a set of $R$-matrix identities. In the continuous limit we reproduce the previously known famil…

Soliton resolution for the coupled complex short pulse equation
Nan Liu, Ran Wang
https://arxiv.org/abs/2505.22210 https://arxiv.org/…

Soliton resolution for the coupled complex short pulse equation
We address the long-time asymptotics of the solution to the Cauchy problem of ccSP (coupled complex short pulse) equation on the line for decaying initial data that can support solitons. The ccSP system describes ultra-short pulse propagation in optical fibers, which is a completely integrable system and posses a $4\times4$ matrix Wadati--Konno--Ichikawa type Lax pair. Based on the $\bar{\partial}$-generalization of the Deift--Zhou steepest descent method, we obtain the long-time asymptotic app…