PROPERTIES OF CONSERVATION-LAWS OF NONLINEAR EVOLUTION-EQUATIONS

A systematic method is developed for evaluating conservation laws of nonlinear evolution equations (NEE's) by employing the time parts of the Bäcklund transformations. The properties of conservation laws are then investigated in detail to obtain the informations about the structure of NEE's themselves. In particular, we focus our attention on the independence of conservation laws. The NEE's considered in this paper are the Boussinesq equation, a model equation for shallow-water waves due to Hirota and Satsuma, the Sawada-Kotera and the Kaup equations and the Ito equation. For all these equations, the inverse scattering transform problems have not been fully solved since the associated isospectral equations become higher-order ones in comparison with the usual Schrödinger equation. © 1990, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.