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A Coupled Korteweg-de Vries System and Mass Exchanges Among Solitons

Peter D. Miller
Department of Mathematics and Statistics
Monash University, Clayton, Vic 3168 Australia

P. L. Christiansen
Department of Mathematical Modeling
The Technical University of Denmark
Lyngby, DK2800 Denmark


We study an N-component, symmetrically coupled system of Korteweg-de Vries (KdV) equations that is integrable in the context of the sl(N+1) AKNS hierarchy. We show how the coupled system can be solved through a combination of the well-known inverse-scattering transform for (one-component) KdV and the solution of a linear equation with nonconstant coefficients. The coupled KdV system may be viewed as a phenomenological model for the sharing of mass among interacting solitons of the (one-component) KdV equation. Results for the scattering theory of solutions of the nonconstant coefficient linear equation arising in the solution of the coupled system are used to quantify the redistribution of mass during soliton collisions within the framework of the coupled KdV model.