A Novel Ermakov–Painlevé II System: ‐Dimensional Coupled NLS and Elastodynamic Reductions

2014/07/21 by Colin Rogers, C. Rogers · 19 citations
Engineering · Mathematics · Physics and Astronomy · #Classical mechanics #Context (archaeology) #Dimensional reduction #Elasticity and Wave Propagation #Geometry #Hyperelastic material #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Physics #Quantum mechanics #Reduction (mathematics) #Superposition principle #Type (biology) #Wave packet

paper · doi:10.1111/sapm.12039

published in Studies in Applied Mathematics 133(2), 214-231 (Wiley)

openalex publication_date 2014/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Wave packet ansätze are introduced into an ‐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.

Citations

• Ermakov–Ray–Reid Reductions of Variational Approximations in Nonlinear Optics
• Sur les équations différentielles du second ordre et du premier degré dont l'intégrale générale est a points critiques fixes

Cited by

• Moving boundary problems for a novel extended mKdV equation. Application of Ermakov-Painlevé II symmetry reduction
• Moving boundary problems with Ermakov symmetry reduction: nonlinear superposition principle and reciprocal transformation applications
• Is Phantom Barrier Crossing Inevitable? A Cosmographic Analysis
• A discretisation of the Ermakov-Painlevé II equation: Dirichlet and Robin-type boundary value problems
• Whitham-Broer-Kaup Systems in Multi-dimensions: Quantum and Resonant NLS Connections
• An Extended Modified Kadomtsov-Petviashvili Equation: Ermakov-Painlevé II Symmetry Reduction with Moving Boundary Application
• On an integrable 2+1-dimensional extended Dym equation: Lax pair, ∂-dressing scheme and modulation
• On integrable Ermakov–Painlevé IV systems

Related

• An Extended Modified Kadomtsov-Petviashvili Equation: Ermakov-Painlevé II Symmetry Reduction with Moving Boundary Application
• Moving boundary problems for a novel extended mKdV equation. Application of Ermakov-Painlevé II symmetry reduction
• Moving boundary problems with Ermakov symmetry reduction: nonlinear superposition principle and reciprocal transformation applications
• Residual Symmetry Reductions and Painlevé Solitons
• Painlevé Integrability And Shifted Nonlocal Reductions Of A Variable Coefficient Coupled HI Mkdv System