Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2006-04-07
Nonlinear Sciences
Exactly Solvable and Integrable Systems
15p., No fig, In: Prof. G. Manev's Legacy in Contemporary Aspects of Astronomy, Gravitational and Theoretical Physics", Eds.:
Scientific paper
Spectral method related to Lame equation with finite-gap potential is used to study the optical cascading equations. These equations are known not to be integrable by inverse scattering method. Due to "partial integrability" two-gap solutions are obtained in terms of products of elliptic functions and are classified in five different families related to eigenvalues of appropriate spectral problem. In special cases, when periodic solutions reduce to localized solitary waves, previously known phase-locked solutions are recovered, and additional one solution is obtained. For vector nonlinear Schrodinger equation n=3 we present exact solutions in a form of multicomponent cnoidal waves.
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