Lyapunov approach to the soliton stability in highly dispersive systems. II: KdV-type equations.(English)Zbl 0972.35518

Summary: The stability of solitons described by fifth order KdV-type 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 $$p<$$8 where $$p$$ is the power of nonlinearity.
For Part I, see ibid. 254-256 (1996; Zbl 0972.35519).

MSC:

 35Q51 Soliton equations 35Q53 KdV equations (Korteweg-de Vries equations)

Zbl 0972.35519
Full Text:

References:

 [1] Karpman, V.I., Phys. lett. A, 215, 254, (1996) [2] Karpman, V.I., Phys. lett. A, 210, 77, (1996) [3] Weinstein, M.I., Commun. math. phys., 87, 567, (1983) [4] Kuznetsov, E.A., Phys. lett. A, 101, 314, (1984) [5] Kuznetsov, E.A.; Rubenchik, A.M.; Zakharov, V.E., Phys. rep., 142, 103, (1986) [6] Karpman, V.I., Phys. lett. A, 186, 303, (1994) [7] Karpman, V.I.; Vanden-Broeck, J.-M., Phys. lett. A, 200, 423, (1995) [8] Ablowitz, M.J.; Segur, H., Solitons and the inverse scattering transform, (1981), SIAM Philadelphia, PA · Zbl 0299.35076
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.