Solitons and poles in the nonlinearity parameter

Abstract

The KdVN-soliton solutions are analysed in terms of the perturbation parameter λ which governs the nonlinearity. They are generated by rational Stieltjes functionsQ ^(N)(λ), each pole of which can be associated with a soliton. The asymptotic emergence of the separate solitons follows at once from the motion of the poles along the negative real λ-axis. Successive diagonal Padé approximants ofQ ^(N)(λ) are considered. They provide a class of approximate solutions with a striking semisoliton like behaviour.