Inverse Problem and Classes of Non-Linear Partial Differential Equations

Abstract

Classes of non-linear partial differential equation solvable by the inverse scattering methods related to the Schrödinger operator and the generalized Zakharov-Shabat operator are presented. Derivations and classification of partial differential equations are different from P. D. Lax’s (Commun. pure appl. Math. 21 (1968) 467) and M. J. Ablowitz et al’s (Phys. Rev. Letters 31 (1973) 125). It is shown that the equations of each class can be derived by a simple successive procedure.