English

Solutions to the Optical Cascading Equations

solv-int 2009-10-31 v1 Exactly Solvable and Integrable Systems Optics

Abstract

Group theoretical methods are used to study the equations describing \chi^{(2)}:\chi^{(2)} cascading. The equations are shown not to be integrable by inverse scattering techniques. On the other hand, these equations do share some of the nice properties of soliton equations. Large families of explicit analytical solutions are obtained in terms of elliptic functions. In special cases, these periodic solutions reduce to localized ones, i.e., solitary waves. All previously known explicit solutions are recovered, and many additional ones are obtained

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Cite

@article{arxiv.solv-int/9812013,
  title  = {Solutions to the Optical Cascading Equations},
  author = {S. Lafortune and P. Winternitz and C. R. Menyuk},
  journal= {arXiv preprint arXiv:solv-int/9812013},
  year   = {2009}
}

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21 pages