SIMILARITY REDUCTIONS FOR VARIABLE-COEFFICIENT COUPLED NONLINEAR SCHRODINGER-EQUATIONS

We categorize classes of coupled nonlinear Schrodinger equations which allow generalized similarity solutions, using the approach of Clarkso n and Kruskal (1989). In all cases, the resulting pair of ordinary dif ferential equations belongs to a single class, presented here as equat ions (2.6). Certain cases allowing solution in terms of familiar funct ions are identified. An alternative approach, presented in section 4, shows that only two conditions need be placed on the four real and two complex coefficients in the governing equations in order that solutio ns generated by an arbitrary solution of the (integrable) NLS equation exist. Applications to some standard coupled systems arising from fib re optics are given.