ASYMPTOTIC EXPANSIONS FOR THE TRANSMISSION COEFFICIENTS OF THE SO-CALLED DAVEY-STEWARTSON-I SYSTEM

Although the system of equations (the so-called Davey-Stewartson 1) -i partial derivative(t)q = 1/2(partial derivative(x)2 + partial derivative(y)2)q + q(partial derivative(y)phi - rq) (partial derivative(x)2 - partial derivative(y)2)phi + 2 partial derivative(y)(rq) = 0 where r = +/-q*, is integrable, only one conservation law is known to exist. This is in stark contrast to other integrable systems where one always has an infinity of such conservation laws. We show by directly expanding the transmission scattering coefficient about k = infinity, that the standard expansion fails to produce any higher conservation laws, but it does produce an infinite hierarchy of dynamical relations.