Abstract
Exact solutions for two classes of coherently coupled nonlinear envelope equations are derived in terms of products of Jacobi elliptic functions. Physical applications are illustrated in the context of nonlinear optics, namely, polarization of light beams and quadratic (or parametric) solitons. Stabilities of these double-humped solitary pulses are studied by direct numerical simulations. The use of computer is crucial, both in terms of symbolic manipulation in the derivation process and in the implementation of numerical schemes in stability consideration.
Acknowledgements
Partial financial support has been provided by the Research Grants Council contract HKU7120/08E and HKU 7118/07E.