Mathematical Annex

  • Andrei LuduEmail author
Part of the Springer Series in Synergetics book series (SSSYN)


This chapter represents a mathematical annex. We briefly remember the properties of the Riccati equation and of some elliptic functions used in soliton theory. We also describe the one-soliton solutions of the KdV and MKdV equations. In the end we present a simple procedure, the so called nonlinear dispersion relation approach, through which one can find information about the relations between amplitude, half-width and speed of a soliton solution of any nonlinear equation (scalar, vector, or system, no matter of the nature of the nonlinearity) without actually solve the equation, providing such an equation admits soliton solutions. Several examples on well known cases are also given in order to illustrate how this procedure works.


Spherical Harmonic Riccati Equation Soliton Solution Nonlinear PDEs Jacobi Elliptic Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of MathematicsEmbry-Riddle Aeronautical UniversityDaytona BeachUSA

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