The Bäcklund and Inverse Scattering Transform of the K-dV Equation with Nonuniformities

抄録

The Bäcklund and inverse scattering transforms are obtained for the Korteweg-de Vries equation with various nonuniformity terms
u_t+6uu_x+u_xxx+[α(x, t)u]_x+γ(t)u=F_x(x,t),
provided that the three functions α(x, t), γ(t) and F_x(x, t) related to the non-uniformities of the system, are constrained by the compatibility condition.