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In the present work the stability criterion for two coupled nonlinear Schrödinger equations having parametric terms is derived. In this investigation, two different types of coupled nonlinear Schrödinger equations are discussed. Two coupled parametric nonlinear Schrödinger equations govern the wave behavior at the self-secondary resonance interaction and other two coupled parametric equations describe the wave-wave interaction at self-cubic resonance case. Stability criterion governing resonance mechanisms is performed in view of temporal periodic perturbations. Moreover, stability criterion at the perfect resonance case is achieved. Further, some numerical calculations are made to screen the stability pictures at the self-second resonance case.
Czasopismo
Rocznik
Tom
Strony
69--85
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
- Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt, yusryeldib52@hotmail.com
Bibliografia
- [1] Doelman, A: Traveling waves in the complex Ginzburg-Landau equation, 1. Nonlinear Sci., (1993), 3, 225-266.
- [2] Whithan, GB: Linear and Nonlinear Waves, (1974), Wiley, New York.
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- [4] Lee, D-S: Second Harmonic resonance on the surface of a magnetohydrodynamie fluid column, Z. Naturforsch., (1999), 54a, 335-342.
- [5] McGoldrick, LF: On the rippling of small waves: A Harmonic nonlinear nearly resonant interaction, J. Fluid Mech., (1972), 52, 725-751.
- [6] Nayfeh, AH: Second-Harmonic resonance in the interaction of an air stream with capillary-gravity waves, J. Fluid Mech., (1973), 59, 803-816.
- [7] Nayfeh, AH, and Saric, WS: Nonlinear Waves in a Kelvin-Hemholtz Flow, J. Fluid Mech., (1972), 55, 311-327.
- [8] Singla, RK, Chhabra, RK and Terhan, SK: Effect of a tangential electric field on the second harmonic resonance in Kelvin-Helmholtz flow, Z. Naturforsch., (1996), 51a, 10-16.
- [9] El-Dib, YO: Nonlinear Wave-Wave Interaction and Stability Criterion for Parametrical Coupled Nonlinear Schrödinger Equations, Nonlinear Dynamics, (2001), 24, 399-418.
- [10] Nayfeh, AH and Mook, DT: Nonlinear Oscillations, (1979), Wiley, New York.
- [11] Feng, JQ and Beard, KV: Resonances of a conducting drop in an alternating electric field, J. Fluid Mech., (1991), 222, 417.
- [12] Tan, B and Boyd JP: Stability and long time evolution of the periodic solutions to the two coupled nonlinear Schrödinger equations, Chaos, Solitons and Fractals, (2001), 12, 721-734.
- [13] Inoue, Y: Nonlinear interaction of dispersive waves with equal group velocity, J. Phys. Soc. Japan, (1977), 34, 243-249.
- [14] Bahakta, JC and Gupta, MR: Stability of solitary wave solutions of simultaneous Schrödinger equations, J. Plasma Phys., (1982), 28, 379-383.
- [15] El-Dib, YO: Nonlinear Mathieu equation and coupled resonance mechanism, Chaos, Solitons and Fractals, 12, 705-720.
- [16] Nayfeh AH: Nonlinear propagation of wave packets on fluid interfaces, J. Appl. Math. Trans. ASME, (1976), 98E, 584-588.
- [17] El-Dib, YO: Note on the stability criterion of a nonlinear partial differential equation of Schrödinger type, Appl. Math. Lett., (1994), 7, 89-92.
- [18] EI-Dib, YO: A parametric nonlinear Schrödinger equation and stability criterion, Chaos, Solitons & Fractals, (1995), 5, 1007-1012.
- [19] El-Dib, YO: Instability of parametric second and third-subharmonic resonance governed by nonlinear Schrödinger equations with complex coefficients, Chaos, Solitons & Fractals, (2000), 11, 1773-1787.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD9-0022-0044