Dual conservation laws of linear planar elasticity theory have been systematically studied based on stress function formalism. By employing generalized symmetry transformation or Lie–B€acklund transformation, a class of new dual conservation laws in planar elasticity have been discovered based on Noether theorem and its Bessel–Hagen generalization. These dual conservation laws represent variati...

We extend the definition of the classical Jacobi polynomials withindexes α,β > −1 to allow α and/or β to be negative integers. We show that the generalized Jacobi polynomials, with indexes corresponding to the number of boundary conditions in a given partial differential equation, are the natural basis functions for the spectral approximation of this partial differential equation. Moreover, the...

Article history: Received 22 May 2009 Received in revised form 13 September 2009 Accepted 15 September 2009 Available online 19 September 2009 Communicated by A.R. Bishop PACS: 02.30.Jr 02.60.Cb 02.60.Lj

Transversely finite sound beams traveling in fluid media with negligible viscous damping and scattering have seven quantities constant along the length of the beam. The simplest of these is the cycle-averaged momentum per unit length of the beam. The seven constant quantities are proved to be invariants from conservation laws. An angular momentum flux density tensor is introduced, in the formul...

The purpose of the present paper is to study presence bifurcations zero-Hopf type at a generalized Genesio differential equation. More precisely, by transforming such equation in first-order system three-dimensional space R3, we are able prove existence bifurcation from which periodic trajectories appear close equilibrium point located origin when parameters and c zero b positive.