Nonisospectral scattering problems: A key to integrable hierarchies

We show that certain partial differential equations associated to nonisospe ctral scattering problems in 2+1 dimensions provide a key to associated int egrable hierarchies of both ordinary and partial differential equations. Th is is illustrated using (an extension of) a known second-order and two new third-order nonisospectral scattering problems. These scattering problems a llow us to derive new hierarchies of integrable partial differential equati ons, in both 1+1 and 2+1 dimensions, together with their underlying linear problems (isospectral and nonisospectral); and also new hierarchies of inte grable ordinary differential equations, again with their underlying linear problems. (C) 1999 American Institute of Physics. [S0022-2488(99)04210-3].