×

Lyapunov approach to the soliton stability in highly dispersive systems. I: Fourth order nonlinear Schrödinger equations. (English) Zbl 0972.35519

Summary: The stability of solitons, described by fourth order nonlinear Schrödinger equations with arbitrary power nonlinearities, is studied by means of the Lyapunov approach. From the results obtained it follows that the solitons are stable at \(pD<4\), where \(p\) is the power of nonlinearity and \(D\) is the number of space dimensions.
Part II, see ibid. 257-259 (1996; Zbl 0972.35518).

MSC:

35Q51 Soliton equations
35Q55 NLS equations (nonlinear Schrödinger equations)

Citations:

Zbl 0972.35518
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Karpman, V.I., Phys. lett. A, 160, 531, (1991)
[2] Karpman, V.I.; Shagalov, A.G., Phys. lett. A, 160, 538, (1991)
[3] Karpman, V.I., Phys. lett. A, 210, 77, (1996)
[4] Karpman, V.I., Phys. rev. E, 53, (1996)
[5] Kuznetsov, E.A.; Rubenchik, A.M.; Zakharov, V.E., Phys. rep., 142, 103, (1986)
[6] Rasmussen, J.J.; Rypdal, K., Phys. scr., 33, 481, (1986)
[7] Wave collapses, (), 1
[8] Turitsyn, S.K., Phys. rev. E, 47, R13, (1993)
[9] Kuznetsov, E.A.; Rasmussen, J.J.; Rypdal, K.; Turitsyn, S.K., Physica D, 87, 273, (1995)
[10] Karpman, V.I., Phys. lett. A, 193, 355, (1994)
[11] V.I. Karpman, to be published.
[12] Weinstein, M.I., Comm. math. phys., 87, 567, (1983)
[13] Ivanov, B.A.; Kosevich, A.M.; Ivanov, B.A.; Kosevich, A.M., Fiz. nizk. temp., Sov. J. low temp. phys., 9, 439, (1983)
[14] Turitsyn, S.K.; Turitsyn, S.K., Teor. mat. fys., Sov. theor. math. phys., 64, 797, (1985)
[15] Karpman, V.I., Phys. lett. A, 215, 257, (1996) · Zbl 0049.14003
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.