zbMATH — the first resource for mathematics

Nonlinear dispersion and compact structures. (English) Zbl 0953.35501
Relaxing the distinguished ordering that underlies the derivation of soliton supporting equations leads to new equations endowed with nonlinear dispersion crucial for the formation and coexistence of compactons, solitons with a compact support, and conventional solitons. Vibrations of the anharmonic mass-spring chain lead to a new Boussinesq equation admitting compactons and compact breathers. The model equation \(u_t+[\delta u+3\gamma u^2/2+u^{1-\omega}(u^\omega u_x)_x]_x+\nu u_{txx}=0\) \((\omega,\nu,\delta,\gamma \text{const})\) admits compactons and for \(2\omega=\nu\gamma=1\) has a bi-Hamiltonian structure. The infinite sequence of commuting flows generates an integrable, compacton’s supporting variant of the Harry Dym equation.

35Q53 KdV equations (Korteweg-de Vries equations)
PDF BibTeX Cite
Full Text: DOI
[1] P. Rosenau, Phys. Rev. Lett. 70 pp 564– (1993) · Zbl 0952.35502
[2] P. Rosenau, in: Nonlinear Coherent Structures in Physics and Biology (1994) · Zbl 0953.35501
[3] V.I. Petviashvili, Sov. Phys. Dokl. 231 pp 17– (1978)
[4] S. Kichenassamy, Siam J. Math. Anal. 23 pp 1141– (1992) · Zbl 0755.76023
[5] P. Rosenau, Prog. Theor. Phys. 79 pp 1028– (1988)
[6] P. Rosenau, Physica (Amsterdam) 27D pp 224– (1987)
[7] P. Rosenau, Phys. Rev. B 36 pp 5868– (1987)
[8] P. Rosenau, Phys. Rev. A 39 pp 6614– (1989)
[9] R. Camassa, Phys. Rev. Lett. 71 pp 1661– (1993) · Zbl 0972.35521
[10] P.J. Olver, in: Applications of Lie Groups to Differential Equations (1986) · Zbl 0588.22001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.