Titlebook: Nonlinear Science and Complexity; J.A. Tenreiro Machado,Albert C.J. Luo,Lino B. Figu Book 2011 Springer Science+Business Media B.V. 2011 N

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Nonclassical and Potential Symmetries for?a?Boussinesq Equation with Nonlinear Dispersiones are derived. We prove that the nonclassical method applied to this equation leads to new symmetries, which can not be obtained by Lie classical method. We also have written the equation in a conserved form and a new class of nonlocal symmetries have been obtained.

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The Role of Invariant Manifolds in?the?Formation of Spiral Arms and Rings in?Barred Galaxieshnique used in celestial mechanics to compute transfer orbits. Thus, our theory is based on the chaotic orbital motion driven by the invariant manifolds associated to the periodic orbits around the hyperbolic equilibrium points. In particular, spiral arms and outer rings are related to the presence

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