Abstract
In continuum mechanics the pseudomomentum is the covariant material momentum whose associated flux in the balance law is Eshelby's “energy-momentum” tensor. The unbalance of pseudomomentum was previously shown to play a basic role in the formulation of configurational forces and path-independent integrals in the theory of elastic inhomogeneities and brittle fracture. Here, it is further shown to provide a fundamental conservation law for dispersive nonlinear elastic systems which exhibit soliton solutions. This is illustrated by both classical and grade-two elasticity with applications to the sine-Gordon, Boussinesq. sine-Gordon -d'Alembert and generalized Zakharov systems encountered in various bulk or surface wave-propagation problems. In these systems the nonconservation of global pseudomomentum may be used for a perturbational approach to nearly integrable systems so as to study the influence of dissipation and external sources (e.g. defects).
Published Version
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