Well-posed Cauchy problem and the Hamiltonian form of (2+1) nonlinear equations integrable by inverse scattering transform

The Hamiltonian form of the (2+1) nonlinear integrable Schrödinger equation and the system of two (2+1) nonlinear analogue of the mKdV equation is proved. A well–posed Cauchy problem is formulated and the solvability of such a problem for the (2+1) nonlinear analogue of the mKdV equation is proved.