A note on the Painleve analysis of a (2+1) dimensional Camassa-Holm equation

We investigate the Painleve analysis for a (2+1) dimensional Camassa-Holm equation. Our results show that it admits only weak Painleve expansions. This then confirms the limitations of the Painleve test as a test for complete integrability when applied to non-semilinear partial differential equations.Comment: Chaos, Solitons and Fractals (Accepted for publication

Legal NLP Meets MiCAR: Advancing the Analysis of Crypto White Papers

In the rapidly evolving field of crypto assets, white papers are essential documents for investor guidance, and are now subject to unprecedented content requirements under the European Union's Markets in Crypto-Assets Regulation (MiCAR). Natural Language Processing (NLP) can serve as a powerful tool for both analyzing these documents and assisting in regulatory compliance. This paper delivers two contributions to the topic. First, we survey existing applications of textual analysis to unregulated crypto asset white papers, uncovering a research gap that could be bridged with interdisciplinary collaboration. We then conduct an analysis of the changes introduced by MiCAR, highlighting the opportunities and challenges of integrating NLP within the new regulatory framework. The findings set the stage for further research, with the potential to benefit regulators, crypto asset issuers, and investors.Comment: Accepted at NLLP2

The Even and Odd Supersymmetric Hunter - Saxton and Liouville Equations

It is shown that two different supersymmetric extensions of the Harry Dym equation lead to two different negative hierarchies of the supersymmetric integrable equations. While the first one yields the known even supersymmetric Hunter - Saxton equation, the second one is a new odd supersymmetric Hunter - Saxton equation. It is further proved that these two supersymmetric extensions of the Hunter - Saxton equation are reciprocally transformed to two different supersymmetric extensions of the Liouville equation.Comment: typos corrected and references added. To appear in Phys.Lett

An integrable shallow water equation with peaked solitons

We derive a new completely integrable dispersive shallow water equation that is biHamiltonian and thus possesses an infinite number of conservation laws in involution. The equation is obtained by using an asymptotic expansion directly in the Hamiltonian for Euler's equations in the shallow water regime. The soliton solution for this equation has a limiting form that has a discontinuity in the first derivative at its peak.Comment: LaTeX file. Figure available from authors upon reques