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

Karpman, V. I.

Phys. Lett., A 215, No. 5-6, 254-256 (1996).

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

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