A Novel Ermakov–Painlevé II System: N+1‐Dimensional Coupled NLS and Elastodynamic Reductions. Issue 2 (21st July 2014)

• Record Type: Journal Article
• Authors: Rogers, Colin
• Is Part Of: Studies in applied mathematics. Volume 133:Issue 2(2014)
• Page Start: 214
• Page End: 231
• Publication Date: 2014-07-21
• Subjects: Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12039
• Languages: English
• ISSNs: 0022-2526

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>Wave packet ansätze are introduced into an <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pghwm43hf2" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00222526:sapm12039:equation:sapm12039-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>‐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.</p> </abstract>