The Cauchy problem for two dimensional difference wave operators is considered with potentials and initial data supported in a bounded region. The large time asymptotic behavior of solutions is obtained. In contrast to the continuous case (when the problem in the Euclidian space is considered, not on the lattice) the resolvent of the corresponding stationary problem has singularities on the continuous spectrum, and they contribute to the asymptotics.
The Cauchy problem for the DMKP equation
Reaction diffusion equations with super-linear absorption: universal bounds, uniqueness for the Cauchy problem, boundedness of stationary solutions
On the Cauchy problem for gravity water waves
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