Geodesic
Nonintegrability of a Fifth-Order Equation with Integrable Two-Body Dynamics
Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 1, pp. 121-136

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a fifth-order partial differential equation (PDE) that is a generalization of the integrable Camassa–Holm equation. This fifth-order PDE has exact solutions in terms of an arbitrary number of superposed pulsons with a geodesic Hamiltonian dynamics that is known to be integrable in the two-body 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. But after demonstrating the nonexistence of a suitable Lagrangian or bi-Hamiltonian structure and obtaining negative results from Painlevé analysis and the Wahlquist–Estabrook method, we assert that this fifth-order PDE is not integrable.
Keywords: Hamiltonian dynamics, nonintegrability, elastic scattering, pulsons. 
@article{TMF_2003_137_1_a12,
     author = {D. D. Holm and A. Hone},
     title = {Nonintegrability of a {Fifth-Order} {Equation} with {Integrable} {Two-Body} {Dynamics}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {121--136},
     publisher = {mathdoc},
     volume = {137},
     number = {1},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_137_1_a12/}
}
TY  - JOUR
AU  - D. D. Holm
AU  - A. Hone
TI  - Nonintegrability of a Fifth-Order Equation with Integrable Two-Body Dynamics
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2003
SP  - 121
EP  - 136
VL  - 137
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2003_137_1_a12/
LA  - ru
ID  - TMF_2003_137_1_a12
ER  - 
%0 Journal Article
%A D. D. Holm
%A A. Hone
%T Nonintegrability of a Fifth-Order Equation with Integrable Two-Body Dynamics
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2003
%P 121-136
%V 137
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2003_137_1_a12/
%G ru
%F TMF_2003_137_1_a12
D. D. Holm; A. Hone. Nonintegrability of a Fifth-Order Equation with Integrable Two-Body Dynamics. Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 1, pp. 121-136. http://geodesic.mathdoc.fr/item/TMF_2003_137_1_a12/