We classify integrable scalar polynomial partial differential equations of second order generaliz... more We classify integrable scalar polynomial partial differential equations of second order generalizing the short pulse equation.
Recently the associated Camassa-Holm (ACH) equation, related to the Fuchssteiner-Fokas-Camassa-Ho... more Recently the associated Camassa-Holm (ACH) equation, related to the Fuchssteiner-Fokas-Camassa-Holm equation by a hodograph transformation, was introduced by Schiff, who derived B\"{a}cklund transformations by a loop group technique and used these to obtain some simple soliton and rational solutions. We show how the ACH equation is related to Schr\"{o}dinger operators and the KdV hierarchy, and use this connection to obtain
In a decision diagram, the average path length (APL) is the average number of nodes on a path fro... more In a decision diagram, the average path length (APL) is the average number of nodes on a path from the root node to a terminal node over all assignments of values to variables. Smaller APL values result in faster evaluation of the ...
... Mario Pavone Ed Clark Fiona Polack Martin Drozda Peter Ross Andries Engelbrecht M. Zubair Sha... more ... Mario Pavone Ed Clark Fiona Polack Martin Drozda Peter Ross Andries Engelbrecht M. Zubair Shafiq Stephanie Forrest Susan Stepney Maoguo Gong Thomas Stibor Fabio Gonzalez Alexander Tarakanov Emma Hart Jon Timmis Andy Hone Andy Tyrrell Christian Jacob Neil ...
Discrete and Continuous Dynamical Systems, Aug 1, 2008
We consider a coupled system of Hamiltonian partial differential equations introduced by Popowicz... more We consider a coupled system of Hamiltonian partial differential equations introduced by Popowicz, which has the appearance of a two-field coupling between the Camassa-Holm and Degasperis-Procesi equations. The latter equations are both known to be integrable, and admit peaked soliton (peakon) solutions with discontinuous derivatives at the peaks. A combination of a reciprocal transformation with Painlevé analysis provides strong evidence that the Popowicz system is non-integrable. Nevertheless, we are able to construct exact travelling wave solutions in terms of an elliptic integral, together with a degenerate travelling wave corresponding to a single peakon. We also describe the dynamics of N-peakon solutions, which is given in terms of an Hamiltonian system on a phase space of dimension 3N.
We classify integrable scalar polynomial partial differential equations of second order generaliz... more We classify integrable scalar polynomial partial differential equations of second order generalizing the short pulse equation.
Recently the associated Camassa-Holm (ACH) equation, related to the Fuchssteiner-Fokas-Camassa-Ho... more Recently the associated Camassa-Holm (ACH) equation, related to the Fuchssteiner-Fokas-Camassa-Holm equation by a hodograph transformation, was introduced by Schiff, who derived B\"{a}cklund transformations by a loop group technique and used these to obtain some simple soliton and rational solutions. We show how the ACH equation is related to Schr\"{o}dinger operators and the KdV hierarchy, and use this connection to obtain
In a decision diagram, the average path length (APL) is the average number of nodes on a path fro... more In a decision diagram, the average path length (APL) is the average number of nodes on a path from the root node to a terminal node over all assignments of values to variables. Smaller APL values result in faster evaluation of the ...
... Mario Pavone Ed Clark Fiona Polack Martin Drozda Peter Ross Andries Engelbrecht M. Zubair Sha... more ... Mario Pavone Ed Clark Fiona Polack Martin Drozda Peter Ross Andries Engelbrecht M. Zubair Shafiq Stephanie Forrest Susan Stepney Maoguo Gong Thomas Stibor Fabio Gonzalez Alexander Tarakanov Emma Hart Jon Timmis Andy Hone Andy Tyrrell Christian Jacob Neil ...
Discrete and Continuous Dynamical Systems, Aug 1, 2008
We consider a coupled system of Hamiltonian partial differential equations introduced by Popowicz... more We consider a coupled system of Hamiltonian partial differential equations introduced by Popowicz, which has the appearance of a two-field coupling between the Camassa-Holm and Degasperis-Procesi equations. The latter equations are both known to be integrable, and admit peaked soliton (peakon) solutions with discontinuous derivatives at the peaks. A combination of a reciprocal transformation with Painlevé analysis provides strong evidence that the Popowicz system is non-integrable. Nevertheless, we are able to construct exact travelling wave solutions in terms of an elliptic integral, together with a degenerate travelling wave corresponding to a single peakon. We also describe the dynamics of N-peakon solutions, which is given in terms of an Hamiltonian system on a phase space of dimension 3N.
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