Symbolic computation on a second-order KdV equation. (May 2016)

• Record Type: Journal Article
• Authors: Lee, C.T.; Lee, C.C.
• Is Part Of: Journal of symbolic computation. Volume 74(2016)
• Page Start: 70
• Page End: 95
• Publication Date: 2016-05
• Subjects: KdV -- Solitary wave -- Multi-soliton solution -- Hirota method; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.06.006
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: The second-order KdV equation was introduced as a model to describe the wave propagation in a weakly nonlinear and weakly dispersive system where the existence of multi-soliton solution is raised as an open question. In this paper, we develop the procedures of the Hirota method for solving the equation and give a rigorous proof in the sense of symbolic computation that the equation can only admit the single solitary wave solution with no chance of obtaining the exact multi-soliton solution. With the effort and results illustrated, we hope it will trigger interests from all disciplines to search for the new type of multi-soliton solutions.