In this chapter we present several applications of the methods given in this book: the center manifold theorem in Chapter 2, the normal form theory in Chapter 3, and the results on reversible bifurcations in Chapter 4. We discuss hydrodynamic instabilities arising in the Navier–Stokes equations in Section 5.1, and we consider in Section 5.2 the question of existence of traveling waves for three different situations: the water-wave problem; reaction-diffusion systems in two dimensions; and one-dimensional lattices.


Solitary Wave Homoclinic Orbit Center Manifold Hydrodynamic Instability Taylor Vortex 


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© EDP Sciences 2011

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesUniversité de Franche-ComtéBesançon CedexFrance
  2. 2.Laboratoire J.A.DieudonnéIUF, Université de NiceNice Cedex 02France

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