Holm, Darryl D., Hone, Andrew N.W. (2003) Nonintegrability of a fifth order equation with integrable twobody dynamics. Theoretical and Mathematical Physics, 137 (1). pp. 14591471. ISSN 00405779. (doi:10.1023/A:1026060924520)
Download (827kB)
Preview



Official URL http://dx.doi.org/10.1023/A:1026060924520 
Abstract
We consider the fifth order partial differential equation (PDE) u4x,t?5uxxt+4ut+uu5x+2uxu4x?5uu3x?10uxuxx+12uux=0, which is a generalization of the integrable CamassaHolm equation. The fifth order PDE has exact solutions in terms of an arbitrary number of superposed pulsons, with geodesic Hamiltonian dynamics that is known to be integrable in the twobody case N=2. Numerical simulations show that the pulsons are stable, dominate the initial value problem and scatter elastically. These characteristics are reminiscent of solitons in integrable systems. However, after demonstrating the nonexistence of a suitable Lagrangian or biHamiltonian structure, and obtaining negative results from Painlev\'{e} analysis and the WahlquistEstabrook method, we assert that the fifth order PDE is not integrable.
Item Type:  Article 

DOI/Identification number:  10.1023/A:1026060924520 
Uncontrolled keywords:  Hamiltonian dynamics, nonintegrability, elastic scattering, pulsons 
Subjects: 
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations Q Science > QA Mathematics (inc Computing science) > QA801 Analytic mechanics 
Divisions:  Faculties > Sciences > School of Mathematics Statistics and Actuarial Science 
Depositing User:  Andrew N W Hone 
Date Deposited:  21 Jun 2014 22:29 UTC 
Last Modified:  07 Jun 2019 10:43 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/41496 (The current URI for this page, for reference purposes) 
 Export to:
 RefWorks
 EPrints3 XML
 BibTeX
 CSV
 Depositors only (login required):