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A novel extension of the canonical 2+1-dimensional Dym equation. Moving boundary problems solvable via Painleve' II Reduction
Colin Rogers, Sandra Carillo
An extension with temporal modulation is presented of the canonical 2 + 1-dimensional solitonic Dym equation as originally introduced by Konopelchenko and Dubrovsky. Application is…
An Extended 2+1-Dimensional Gardner Equation: On Moving Boundary Problems Solvable via Ermakov-Painlevé II Symmetry Reduction
Colin Rogers, Sandra Carillo
A class of moving boundary problems of Stefan-type for an extension of the 2+1- dimensional Gardner equation is shown to be amenable to exact solution by application of a Ermakov-…
Ermakov-Painleve' II Symmetry Reduction of a Class of Moving Boundary Problems for a Reciprocal Extended mKdV Equation
Colin Rogers, Sandra Carillo
A reciprocal transformation is applied to link an integrable extension of the classical solitonic mKdV to a novel nonlinear evolution equation incorporating a source term. Applicat…
Moving Boundary Problems for a Cuspon Equation and Reciprocal Associates: Exact Solution via Painleve' Symmetry Reduction
Colin Rogers, Sandra Carillo
Here classes of moving boundary problems of Stefan-type for both an established non-linear evolution equation of cuspon theory and novel reciprocally linked solitonic equations are…
Soliton equations: admitted solutions and invariances via Bäcklund transformations
Sandra Carillo, Cornelia Schiebold
A couple of applications of Bäcklund transformations in the study of nonlinear evolution equations is here given. Specifically, we are concerned about third order nonlinear evoluti…