A Novel Ermakov–Painlevé II System: N+1‐Dimensional Coupled NLS and Elastodynamic Reductions. Issue 2 (21st July 2014) - Rogers, Colin
<x xml:space="preserve">Abstract</x> Wave packet ansätze are introduced into an <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pghwm43hf2" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />N+1</alternatives>‐dimensional Manakov‐type system and key invariants are isolated. Reduction is made to a novel coupled Ermakov–Painlevé II system and an algorithm presented for the derivation of wave packet representations via the classical Ermakov nonlinear superposition principle. Application of the procedure in the context of certain transverse wave motions in a generalized Mooney–Rivlin hyperelastic material is likewise shown to lead an Ermakov–Painlevé II reduction.