×
Kraenkel, R. A.; Senthilvelan, M.; Zenchuk, A. I.

On the integrable perturbations of the Camassa-Holm equation. (English) Zbl 1052.37058

J. Math. Phys. 41, No. 5, 3160-3169 (2000).
Summary: The authors present an investigation of the nonlinear partial differential equations which are asymptotically representable as a linear combination of the equations from the Camassa-Holm hierarchy. For this purpose they use the infinitesimal transformations of dependent and independent variables of the original PDE. This approach is helpful for the analysis of the systems of the PDE which can be asymptotically represented as the evolution equations of polynomial structure.

Cited in 6 Documents

MSC:

37K55 Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems
PDF BibTeX XML Cite
\textit{R. A. Kraenkel} et al., J. Math. Phys. 41, No. 5, 3160--3169 (2000; Zbl 1052.37058)
Full Text: DOI

References:

[1] DOI: 10.1103/PhysRevLett.71.1661 · Zbl 0972.35521
[2] DOI: 10.1016/0167-2789(95)00133-O · Zbl 1194.35363
[3] DOI: 10.1016/0167-2789(95)00133-O · Zbl 1194.35363
[4] DOI: 10.1016/0167-2789(81)90004-X · Zbl 1194.37114
[5] DOI: 10.1007/BF00739423 · Zbl 0808.35124
[6] DOI: 10.1016/0167-2789(96)00048-6 · Zbl 0900.35345
[7] Li Y. A., Discrete Cont. Dyn. Syst. 3 pp 419– (1997)
[8] Li Y. A., Discrete Cont. Dyn. Syst. 4 pp 159– (1998)
[9] DOI: 10.1134/1.567940
[10] DOI: 10.1088/0305-4470/32/25/313 · Zbl 0941.35094
[11] DOI: 10.1016/0375-9601(85)90500-6
[12] DOI: 10.1016/0375-9601(85)90207-5 · Zbl 1177.37058
[13] DOI: 10.1143/JPSJ.58.4322
[14] DOI: 10.1364/OL.15.001443
[15] DOI: 10.1103/PhysRevLett.66.161 · Zbl 0968.35513
[16] DOI: 10.1016/0375-9601(87)90227-1
[17] DOI: 10.1103/PhysRevE.58.2526
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.