3 papers
nlin.SI2026
Two-peakon dynamics in the Clifford algebra generalization of the Camassa-Holm equation
Alexander Karlson, Jacek Szmigielski
We study the dynamics of a two-component perturbation of the Camassa--Holm equation arising from a reformulation of the Euler--Bernoulli beam problem, recently extended to a genera…
nlin.SI2026
Vector peakon equations and isospectral flows in Clifford algebras
Andrew N. W. Hone, Vladimir S. Novikov, Jacek Szmigielski
Starting from a spectral problem posed in a Clifford algebra with generators and Euclidean signature, we study an integrable, coupled system of PDEs that can be viewed as a vec…
nlin.SI2025
A generalization of the beam problem: Connection to multi-component Camassa-Holm dynamics
Richard Beals, Jacek Szmigielski
We extend the Euler-Bernoulli beam problem, formulated as a matrix string equation with a matrix-valued density, to a setting where the density takes values in a Clifford algebra,…