Interactions of solitons in nonintegrable systems: Direct perturbation method and applications

Abstract Problems of approximate description of soliton interaction in nonintegrable systems are discussed. It is shown that in an arbitrary Lagrangian system in the first nontrivial order of the small parameter asymptotic scheme for a system of solitons with close velocities a Lagrangian may be introduced analogous to that for classical particles with a pair interaction potential. A classification of possible types of soliton interaction is given and criteria of the existence of bound states are formulated. A possibility of generalization of approximated description of soliton interaction in the multidimensional case is noted.