Internal friction between solitons in near-integrable systems

We study inelastic interactions (internal friction) between two solitons in a system described by a near-integrable generalized nonlinear Schr\"odinger equation. An analytic method for calculating the radiation intensity and the rates of amplitude changes of two interacting solitons is proposed. This method shows that, in the limit of zero angle of collision, the amplitude of the smaller soliton decays so that it is inversely proportional to the cube root of the propagation distance. The radiation losses associated with the internal friction of two solitons occur at the expense of the smaller soliton. Half of the energy lost from the smaller soliton is radiated and half goes to the larger soliton. The results obtained by use of our analytic method are in excellent agreement with numerical simulations.