Breathers and limit solutions of the nonlinear lumped self-dual network equation

More general Casoratian conditions for the nonlinear lumped self-dual network equation are proved via its bilinear Bäcklund transformation. Limit solutions and breathers are the special cases in the solution list related to the new Casoratian conditions. By asymptotic analysis we give a clear description on 2-soliton interactions and the relationship between 2-soliton solution and the simplest limit solution. Dynamics of breathers and limit breathers are also investigated.