Complexiton solutions to integrable equations

Details Complexiton solutions to integrable equations Complexiton solutions to integrable equations

2005-02-17

arxiv.org/abs/nlin/0502035v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 Pages, to appear in Nonlinear Analysis

Scientific paper

Complexiton solutions (or complexitons for short) are exact solutions newly introduced to integrable equations. Starting with the solution classification for a linear differential equation, the Korteweg-de Vries equation and the Toda lattice equation are considered as examples to exhibit complexiton structures of nonlinear integrable equations. The crucial step in the solution process is to apply the Wronskian and Casoratian techniques for Hirota's bilinear equations. Correspondence between complexitons of the Korteweg-de Vries equation and complexitons of the Toda lattice equation is provided.

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