2005/02/17 by Wen-Xiu Ma, Wen‐Xiu Ma, Ma, Wen-Xiu
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fractional Differential Equations Solutions #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS) #nlin.PS #nlin.SI
paper · pdf · doi:10.48550/arxiv.nlin/0502035
11 Pages, to appear in Nonlinear Analysis
arxiv created 2005/02/17 · openalex publication_date 2005/02/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.