We describe an approach called the “weak asymptotics method” to construct multisoliton asymptotic solutions for essentially nonintegrable equations with small dispersion. This paper contains a detailed review of the method and a perturbation theory to describe the interaction of distorted solitons for equations with small perturbations. All constructions have been realized for the gKdV equation with the nonlinearity uμ, μ ∈ (1, 5).
Part of the book: Complexity in Biological and Physical Systems