302 citations · 1k across the 44 of their papers we have counts for
45 papers
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…
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…
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,…
On the multipeakon system of a two-component Novikov equation
Xiang-Ke Chang, Jacek Szmigielski
We are exploring variations of the Novikov equation that have weak solutions called peakons. Our focus is on a two-component Novikov equation with a non-self-adjoint La…
A view of the peakon world through the lens of approximation theory
Hans Lundmark, Jacek Szmigielski
Peakons (peaked solitons) are particular solutions admitted by certain nonlinear PDEs, most famously the Camassa-Holm shallow water wave equation. These solutions take the form of…
A 2-component Camassa-Holm equation, Euler-Bernoulli Beam Problem and Non-Commutative Continued Fractions
Richard Beals, Jacek Szmigielski
A new approach to the Euler-Bernoulli beam based on an inhomogeneous matrix string problem is presented. Three ramifications of the approach are developed: (1) motivated by an anal…