Optical solitons in presence of higher-order effects

Abstract

In this paper, we seek special soliton solutions of so-called Higher-Order Nonlinear Schroedinger Equation, which describes the propagation of light waves in nonlinear optical media. Using a developed Jacobi elliptic function expansion method described in [8], we show that in the case of four-order dispersion these traveling wave solutions do not exist. As a byproduct, we regain the results obtained by other authors [8, 9] for the case when only the dispersion to the third order is taken into account. Full Text: PDF References C. Long Van, M. Trippenbach, "New Optical Solitary waves in the higher order nonlinear Schroedinger Equation", Scientific Bulletin 126, Technical University of Zielona Gora, Poland 2001, p.19 (Cao Long Van ed.). V. Cao Long, H. Nguyen Viet, M. Trippenbach, K. Dinh Xuan,"Propagation Technique for Ultrashort Pulses I", Computational Methods in Science and Technology 14(1), 5 (2008) V. Cao Long, H. Nguyen Viet, M. Trippenbach, K. Dinh Xuan,"Propagation Technique for Ultrashort Pulses II ", Computational Methods in Science and Technology 14(1), 13 (2008) V. Cao Long, H. Nguyen Viet, M. Trippenbach, K. Dinh Xuan,"Propagation Technique for Ultrashort Pulses III ", Computational Methods in Science and Technology 14(1), 21 (2008) C. Long Van, P. P. Goldstein, "A concise Course in nonlinear Partial Differential Equations" (University of Zielona Gora 2008). A. V. Buryak and Yu. S. Kivshar,"Solitons due to second harmonic generation", Phys. Lett. A 197, 407 (1995) [CrossRef] M. Trippenbach, M. Matuszeski, E. Infreld, Cao Long Van, R. S. Tasgal, J. B. Band,"Enhancement of third harmonic generation by wave vector mismatch to counter phase- modulation ", Optics Comm. 229, 391 (2004) [CrossRef] S. A. El-Wakil, M.A. Abdou, A. Elhanbaly,"New solitons and periodic wave solutions for nonlinear evolution equations", Phys. Lett. A 353, 40 (2006) [CrossRef] Q. Yang, C.Q. Dai, J. F. Zhang,"Higher-Order Effects Induced Optical Solitons in Fiber", International Journal of Theoretical Physics 44, 1117 (2005) [CrossRef]