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This article is cited in 15 scientific papers (total in 15 papers)
Nonintegrability of a Fifth-Order Equation with Integrable Two-Body Dynamics
D. D. Holma, A. Honeb a Los Alamos National Laboratory
b University of Kent
Abstract:
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.
Citation:
D. D. Holm, A. Hone, “Nonintegrability of a Fifth-Order Equation with Integrable Two-Body Dynamics”, TMF, 137:1 (2003), 121–136; Theoret. and Math. Phys., 137:1 (2003), 1459–1471
Linking options:
https://www.mathnet.ru/eng/tmf250https://doi.org/10.4213/tmf250 https://www.mathnet.ru/eng/tmf/v137/i1/p121
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