Similarity reductions for variable-coefficient coupled nonlinear Schrodinger equations

The authors categorize classes of coupled nonlinear Schrodinger equations which allow generalized similarity solutions, using the approach of Clarkson and Kruskal (1989). In all cases, the resulting pair of ordinary differential equations belongs to a single class. Certain cases allowing solution in terms of familiar functions are identified. An alternative approach shows that only two conditions need be placed on the four real and two complex coefficients in the governing equations in order that solutions generated by an arbitrary solution of the (integrable) NLS equation exist. Applications to some standard coupled systems arising from fibre optics are given.