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Embedded solitons: a new type of solitary wave

Author

Listed:
  • Yang, J.
  • Malomed, B.A.
  • Kaup, D.J.
  • Champneys, A.R.

Abstract

We describe a novel class of solitary waves in second-harmonic-generation models with competing quadratic and cubic nonlinearities. These solitary waves exist at a discrete set of values of the propagation constants, being embedded inside the continuous spectrum of the linear system (“embedded solitons”, ES). They are found numerically and, in a reduced model, in an exact analytical form too. We prove analytically and verify by direct simulations that the fundamental (single-humped) ESs are linearly stable, but are subject to a weak nonlinear one-sided instability. In some cases, the nonlinear instability is so weak that ES is a virtually stable object. Multi-humped embedded solitons are found too, all being linearly (strongly) unstable.

Suggested Citation

  • Yang, J. & Malomed, B.A. & Kaup, D.J. & Champneys, A.R., 2001. "Embedded solitons: a new type of solitary wave," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 56(6), pages 585-600.
    • Handle: RePEc:eee:matcom:v:56:y:2001:i:6:p:585-600
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    Cited by:

    1. Ilison, Lauri & Salupere, Andrus, 2009. "Propagation of sech2-type solitary waves in hierarchical KdV-type systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(11), pages 3314-3327.
    2. Zhao Li & Chen Peng, 2023. "Dynamics and Embedded Solitons of Stochastic Quadratic and Cubic Nonlinear Susceptibilities with Multiplicative White Noise in the Itô Sense," Mathematics, MDPI, vol. 11(14), pages 1-11, July.

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