Abstract
Many models for physical phenomena in oceanography, atmospheric dynamics, optical fibre transmission, nerve conduction, acoustical and gas dynamic flows are conservative translation-invariant evolution equations with a Hamiltonian structure. Solitary waves and fronts form an important class of solutions of such equations and the calculus of variations, critical point theory and symplectic structure have played a major role in the analysis of their stability and instability. For example, the characterisation of solitary waves as critical points of the Hamiltonian (energy) constrained to level sets of the momentum (or momentum and other constants of motion) leads to a powerful framework for proving nonlinear Lyapunov stability – when the second variation, evaluated at the constrained critical point, has a finite number of negative eigenvalues (e.g. BENJAMIN2, BONA3, HOLM ET AL14, GRILLAKIS ET AL12, 13, MADDOCKS & SACHS16 and references therein)…