Dbar-dressing Method To Discrete Three-wave Equation

The dressing method based on the nonlocal Dbar-problem is used to study one kind of(2+1)-dimensional discrete three-wave equation.The advantage of the dressing method is not only to derive the nonlinear integrable equations,but also to give their explicit so-lutions.In the paper,starting from two covariant derivatives operators and one translation operator,we construct the Lax pair associated with one kind of(2+1)-dimensional three-wave equation,and the equation.Then in the frame of nonlocal Dbar-problem,and by choosing the suitable Dbar data,we obtain the representation of the potentials in terms of the scattering data.Finally,we give the explicit solutions of the(2+1)-dimensional discrete three-wave equation by virtue of introducing the symmetry constraint.