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Optimized Algorithm for Petviashvili’s Method for Finding Solitons in Photonic Lattices

In: Approximation and Computation

Author

Listed:
  • Raka Jovanović

    (Institute of Physics)

  • Milan Tuba

    (Megatrend University)

Abstract

In this paper we present an improved algorithm for Petviashvili’s heuristic numerical method for finding solitons in optically induced photonic lattices. Petviashvili’s method is usually used for approximating stationary solutions of nonlinear wave equations to construct numerically the solitary wave solutions such as solitons, lumps, and vortices. We developed and implemented a general software simulator designed for finding solitons in photonic lattices. The Petviashvili’s method is first modified by adding a stabilizing factor that greatly increases stability of the original method. Our software simulator implementation includes a number of criteria for recognizing, at an early stage, divergent or very slowly convergent cases. These criteria, that include Absence of stabilization, Slow convergence, Long interval of instability and Seesaw, significantly lower the overall calculation time.

Suggested Citation

  • Raka Jovanović & Milan Tuba, 2010. "Optimized Algorithm for Petviashvili’s Method for Finding Solitons in Photonic Lattices," Springer Optimization and Its Applications, in: Walter Gautschi & Giuseppe Mastroianni & Themistocles M. Rassias (ed.), Approximation and Computation, pages 393-400, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-6594-3_25
    DOI: 10.1007/978-1-4419-6594-3_25
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