×

zbMATH — the first resource for mathematics

Asymptotic behavior of a weakly dissipative modified two-component Dullin-Gottwald-Holm system. (English) Zbl 06892560
Summary: In this paper, we consider the asymptotic behavior of a weakly dissipative modified two-component Dullin-Gottwald-Holm (mDGH2) system. We derive the asymptotic behavior of the solution at infinity expressed in exponential and algebraic forms. It is shown that there are some results about these properties of the strong solutions in \(L^\infty\)-space.

MSC:
34 Ordinary differential equations
35 Partial differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Holm, D.; Náraigh, L.Ó.; Tronci, C., Phys. Rev. E, 79, 016601, (2009)
[2] Camassa, R.; Holm, D., Phys. Rev. Lett., 71, 1661-1664, (1993)
[3] Camassa, R.; Holm, D.; Hyman, J., Adv. Appl. Mech., 31, 1-33, (1994)
[4] Fokas, A.; Fuchssteiner, B., Physica D, 4, 47-66, (1981)
[5] Constantin, A.; Lannes, D., Arch. Ration. Mech. Anal., 192, 165-186, (2009)
[6] Novruzov, E., J. Differential Equations, 261, 1115-1127, (2016)
[7] Himonas, A.; Misiolek, G.; Ponce, G.; Zhou, Y., Commun. Math. Phys., 271, 2, 511-522, (2007)
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.