Bäcklund Transformations and Superposition Principles in Nonlinear Elastodynamics

DOI10.1111/j.1467-9590.2009.00465.xzbMath1187.37105OpenAlexW2033825012MaRDI QIDQ3406736

Wolfgang K. Schief, Colin Rogers

Publication date: 19 February 2010

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/j.1467-9590.2009.00465.x

zbMATH Keywords

superposition principlenonlinear elastodynamicsBäcklund transformation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Dynamical systems in classical and celestial mechanics (37N05) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (5)

Nonlinear wave interactions in a macroscopic production model ⋮ An exact description of nonlinear wave interaction processes ruled by \(2\times 2\) hyperbolic systems ⋮ On Madelung systems in nonlinear optics: A reciprocal invariance ⋮ The Korteweg capillarity system. Integrable reduction via gauge and reciprocal links ⋮ Cnoidal and gausson phenomena in nonlinear elastodynamics

Cites Work

• Unnamed Item
• A novel class of model constitutive laws in nonlinear elasticity: construction via Loewner theory
• Generation of solutions of systems of partial differential equations by composition of infinitesimal Bäcklund transformations
• Large amplitude waves in bounded media I. Reflexion and transmission of large amplitude shockless pulses at an interface
• Large amplitude waves in bounded media II. The deformation of an impulsively loaded slab: the first reflexion
• Large amplitude waves in bounded media III. The deformation of an impulsively loaded slab: the second reflexion
• AFFINE SOLITONS: A RELATION BETWEEN TAU FUNCTIONS, DRESSING AND BÄCKLUND TRANSFORMATIONS
• On generalized Loewner systems: Novel integrable equations in 2+1 dimensions
• Loewner Transformations: Adjoint and Binary Darboux Connections
• Isothermic Surfaces in Spaces of Arbitrary Dimension: Integrability, Discretization, and Bäcklund Transformations—A Discrete Calapso Equation

This page was built for publication: Bäcklund Transformations and Superposition Principles in Nonlinear Elastodynamics