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Canonical propagators for nonlinear systems: Theory and sample applications

Part of the Lecture Notes in Mathematics book series (LNM,volume 1460)

Abstract

A new canonical formalism for solving general nonlinear systems is presented. Fundamental to this formalism is the construction of forward (advanced) and backward (retarded) propagators that yield the problem's solution exactly, by propagating volume, surface, and initial sources. These propagators also satisfy reciprocity and semigroup properties. Therefore, they represent a generalization to nonlinear systems of the Green's functions from linear theory. Several examples are presented to illustrate the application of the algorithm as well as its numerical advantages over alternative methods.

Keywords

  • Nonlinear System
  • Riccati Equation
  • Vries Equation
  • Propagator Method
  • General Nonlinear System

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References

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© 1991 Springer-Verlag

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Cacuci, D.G., Protopopescu, V. (1991). Canonical propagators for nonlinear systems: Theory and sample applications. In: Toscani, G., Boffi, V., Rionero, S. (eds) Mathematical Aspects of Fluid and Plasma Dynamics. Lecture Notes in Mathematics, vol 1460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091360

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  • DOI: https://doi.org/10.1007/BFb0091360

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53545-4

  • Online ISBN: 978-3-540-46779-3

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