2005/09/30 by A. Parker · 1 citation
Physics and Astronomy · Chemistry · Mathematics · #Nonlinear Waves and Solitons #Molecular spectroscopy and chirality #Algebraic structures and combinatorial models #Soliton #Bilinear interpolation #Transformation (genetics) #Camassa–Holm equation #Work (physics) #Mathematics #Representation (politics) #Set (abstract data type) #Mathematical physics #Mathematical analysis #Integrable system #Applied mathematics #Physics #Chemistry #Thermodynamics #Quantum mechanics #Nonlinear system #Computer science
paper · doi:10.1098/rspa.2005.1537
openalex publication_date 2005/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the concluding study (designated III), we modify the direct bilinear transformation method for solving the Camassa–Holm (CH) equation that was set down in part II of this work. We demonstrate its efficacy for finding analytic multisoliton solutions of the equation and give explicit expressions for the first few solitons. It is shown that, at each order N , the N -soliton has a non-standard representation that is characterized by an ‘extra’ parameter. The stucture of this parameter is investigated and a procedure for constructing the general N -soliton solution of the CH equation is presented.