On pattern structures of the N-soliton solution of the discrete KP equation over a finite field

The existence and properties of coherent pattern in the multisoliton solutions of the dKP equation over a finite field are investigated. To that end, starting with an algebro-geometric construction over a finite field, we derive a 'travelling wave' formula for N-soliton solutions in a finite field. However, despite it having a form similar to its analogue in the complex field case, the finite-field solutions produce patterns essentially different from those of classical interacting solitons