Geometrically implied nonlinearities in mechanics and field theory. (English) Zbl 1126.70014

Mladenov, Ivaïlo (ed.) et al., Proceedings of the 8th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 9–14, 2006. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-37-0/pbk). 48-118 (2007).
The concept of essential nonlinearity is addressed, where the nonlinear system is not decomposable into a linear one plus a small nonlinear correction. The relationship of essential nonlinearity to large symmetry groups is investigated.
For the entire collection see [Zbl 1108.53003].


70S10 Symmetries and conservation laws in mechanics of particles and systems
70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics