5 papers
A novel 2+1-dimensional extended Dym equation: moving boundary problems solvable via Painlevé II symmetry reduction
Colin Rogers, Pablo Amster
A novel 2+1-dimensional extension of the solitonic Dym equation is shown to admit a Painlevé II symmetry reduction which permits the exact solution of a class of Stefan-type movin…
An Extended Modified Kadomtsov-Petviashvili Equation: Ermakov-Painlevé II Symmetry Reduction with Moving Boundary Application
Colin Rogers, Pablo Amster
Here, a novel 2+1-dimensional nonlinear evolution equation with temporal modulation is introduced which admits integrable Ermakov-Painlevé II symmetry reduction. Application is ma…
On an integrable 2+1-dimensional extended Dym equation: Lax pair, -dressing scheme and modulation
Boris Konopelchenko, Colin Rogers, Pablo Amster
In 1+1-dimensions, an extension of the canonical solitonic Dym equation has previously been derived both in a geometric torsion evolution context and in the analysis of peakon soli…
An abstract Gronwall inequality on a Banach lattice
Pablo Amster, Julián Epstein
An abstract version of the celebrated inequality is described by means of the spectral bound of an operator defined on a Banach lattice. As a consequence, uniqueness and continuous…
A discretisation of the Ermakov-Painlevé II equation: Dirichlet and Robin-type boundary value problems
Pablo Amster, Colin Rogers
Two-point boundary value problems for a discrete Ermakov-Painlevé II equation are analysed by means of topological methods. In addition, an alternative variational approach is det…