91 citations · 698 across the 49 of their papers we have counts for
57 papers
Similarity reductions of peakon equations: integrable cubic equations
L. E. Barnes, A. N. W. Hone, M. Senthilvelan +1
We consider the scaling similarity solutions of two integrable cubically nonlinear partial differential equations (PDEs) that admit peaked soliton (peakon) solutions, namely the mo…
Similarity reductions of peakon equations: the -family
Lucy E. Barnes, Andrew N. W. Hone
The -family is a one-parameter family of Hamiltonian partial differential equations of non-evolutionary type, which arises in shallow water wave theory. It admits a variety of s…
Casting light on shadow Somos sequences
Andrew N. W. Hone
Recently Ovsienko and Tabachnikov considered extensions of Somos and Gale-Robinson sequences, defined over the algebra of dual numbers. Ovsienko used the same idea to construct so-…
Growth of Mahler measure and algebraic entropy of dynamics with the Laurent property
Andrew N. W. Hone
We consider the growth rate of the Mahler measure in discrete dynamical systems with the Laurent property, and in cluster algebras, and compare this with other measures of growth.…
Deformations of cluster mutations and invariant presymplectic forms
Andrew N. W. Hone, Theodoros E. Kouloukas
We consider deformations of sequences of cluster mutations in finite type cluster algebras, which destroy the Laurent property but preserve the presymplectic structure defined by t…
Heron triangles with two rational medians and Somos-5 sequences
Andrew N. W. Hone
Triangles with integer length sides and integer area are known as Heron triangles. Taking rescaling freedom into account, one can apply the same name when all sides and the area ar…