Hamiltonian approach to the soliton-soliton interaction and for a classical solitonic gas

The known stationary solutions of the parametrically driven and damped nonlinear Schrödinger equation (PDDNLS) have been used to calculate the interaction potential and the interaction law of pairs of solitons from a strictly theoretical point of view. In agreement with the numerical simulations reported in the literature, our results reveal that the phase difference between solitons plays an important role in their dynamics (this can be either zero or π), and that the two-soliton interaction is very weak and exponential type. Finally, the model was applied to a solitonic gas to find its thermodynamics and numerical simulations were also performed to study the dynamics of this gas.