A nonconfocal involutive system and constrained flows associated with the MKdV- equation

By symmetry constraints, new finite-dimensional integrable systems are deduced from a Lax representation of the MKdV(-) equation, whose two terms containing spatial derivatives have the same sign. Lax representations are presented for the resulting finite-dimensional integrable systems and an r-matrix formulation is established for the corresponding Lax operator. From the Lax operator, a nonconfocal involutive system of functionally independent polynomial functions is constructed. Solutions of the MKdV(-) can be obtained by the method of separation of variables. (C) 2002 American Institute of Physics.