21 citations · 51 across the 4 of their papers we have counts for
4 papers
The r-Hunter-Saxton equation, smooth and singular solutions and their approximation
Colin Cotter, Jacob Deasy, Tristan Pryer
In this work we introduce the r-Hunter-Saxton equation, a generalisation of the Hunter-Saxton equation arising as extremals of an action principle posed in L_r. We characterise sol…
Waltzing peakons and compacton pairs in a cross-coupled Camassa-Holm equation
Colin Cotter, Darryl Holm, Rossen Ivanov +1
We consider singular solutions of a system of two cross-coupled Camassa-Holm (CCCH) equations. This CCCH system admits peakon solutions, but it is not in the two-component CH integ…
The Square Root Depth Wave Equations
Colin C. Cotter, Darryl D. Holm, James R. Percival
We introduce a set of coupled equations for multilayer water waves that removes the ill-posedness of the multilayer Green-Naghdi (MGN) equations in the presence of shear. The new w…
A General Approach for Producing Hamiltonian Numerical Schemes for Fluid Equations
Colin Cotter
Given a fluid equation with reduced Lagrangian which is a functional of velocity $\MM{u}$ and advected density given in Eulerian coordinates, we give a general method for s…