Using an integrable Gardner equation as an example, a perturbation theory is developed for systems in which limiting-amplitude solitons exist in the form of a pair of distanced kinks. Approximate equations describing multisoliton interactions are derived and further used for modeling the evolution of an arbitrary set of solitons. The results are compared with an exact solution and numerical results. The theory is applied to data from observation of a train of strongly nonlinear internal waves in the ocean.

• Received 9 September 2003

DOI:https://doi.org/10.1103/PhysRevE.69.016614