Matrix Kp Equation : Matrix Identities and Explicit Non-Singular Solutions

A new version of the Bäcklund-Darboux transformation for the matrix Kadomtsev-Petviashvili equation is used to construct and study explicit multi-parameter solutions and wave functions (in terms of the matrix exponents). A class of the self-adjoint non-singular solutions of KP I is introduced using the controllability notion from the system theory. A subclass of the rationally decaying self-adjoint non-singular solutions is studied, in particular. Several results prove new in the scalar case also.J. Phys. A (2003), 5023-5024