Long-range interacting solitons: pattern formation and nonextensive thermostatistics

The nonlinear Klein–Gordon equation with a different potential that satisfies the degeneracy properties discussed in this paper possesses solitonic solutions that interact with long-range forces. We generalize the Ginzburg–Landau equation in such a way that the topological defects supported by this equation present long-range interaction both in D=1 and D>1. Finally, we construct a system of two equations with two complex order parameters for which the interaction forces between the topological defects decay so slowly that the system enters the nonextensivity regime.