Scattering theory for the operator partial deriv/((partial deriv)t) - (partial deriv)~2/((partial deriv)x~2) - (partial deriv)~2/((partial deriv)y~2)

摘要

In this article, following the (partial deriv)-bar-method of scattering theory, we develop the direct and inverse scattering theory for the operator partial deriv/((partial deriv)t) - (partial deriv)~2/((partial deriv)x~2) - (partial deriv)~2/((partial deriv)y~2). Due to lack of symmetry of the operator, we have to partition the kernel of the inverse scattering operator into several pieces and estimate. After developing the theory of direct and inverse scattering, we show that there is a one-to-one correspondence between the solutions of the direct scattering problem and those of the inverse scattering problem.