Lax Integrability of the Modified Camassa-Holm Equation and the Concept of Peakons. Issue 4 (1st October 2016)

• Record Type: Journal Article
• Authors: Chang, Xiangke; Szmigielski, Jacek
• Is Part Of: Journal of nonlinear mathematical physics. Volume 23:Issue 4(2016)
• Page Start: 563
• Page End: 572
• Publication Date: 2016-10-01
• Subjects: Weak solutions -- peakons -- distributions; 35D30 -- 35Q51 -- 37J35 -- 35Q53; Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2016.1248156
• Languages: English
• ISSNs: 1402-9251

Abstract

Abstract : In this Letter we propose that for Lax integrable nonlinear partial differential equations the natural concept of weak solutions is implied by the compatibility condition for the respective distributional Lax pairs. We illustrate our proposal by comparing two concepts of weak solutions of the modified Camassa-Holm equation pointing out that in the peakon sector (a family of non-smooth solitons) only one of them, namely the one obtained from the distributional compatibility condition, supports the time invariance of the Sobolev H 1 norm.