N. Manganaro et Df. Parker, SIMILARITY REDUCTIONS FOR VARIABLE-COEFFICIENT COUPLED NONLINEAR SCHRODINGER-EQUATIONS, Journal of physics. A, mathematical and general, 26(16), 1993, pp. 4093-4106
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.