Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws

Abstract

It is shown that inverse method, Backlund transformation and an infinite number of conservation laws are closely related. The derivation of Backlund transformation from the fundamental equations of inverse method is explicitly shown. Also it is shown that conser vation la~ is obtained in a simple way from the. Riccati form of inverse method and the derivation of conservation law from Backlund transformation is possible. I. Introduction During the last decade, study of the nonlinear wave phenomena has made a remarkable stride. 1 ) It has been confirmed that several simple nonlinear partial differential equations are widely applicable to the various nonlinear phenomena in physics. Also it has been shown that we have a class of nonlinear partial differential equations which have common properties: 1) The equations can be solved exactly by the "inverse method" and yield the so-called N-soliton solutions.