Soliton-like solutions of a derivative nonlinear Schrödinger equation with variable coefficients in inhomogeneous optical fibers
- 328 Downloads
Under investigation in this paper is a derivative nonlinear Schrödinger equation with variable coefficients, which governs the propagation of the subpicosecond soliton pulses in inhomogeneous optical fibers. Through the nonisospectral Kaup–Newell scheme, the Lax pair is constructed with some constraints on the variable coefficients. Under the integrable conditions, bright one- and multi-soliton-like solutions are derived via the Hirota method. By suitably choosing the dispersion coefficient function, several types of inhomogeneous solitons are obtained in, respectively: (1) exponentially decreasing dispersion profile, (2) linearly decreasing dispersion profile, (3) exponentially increasing dispersion profile, and (4) periodically fluctuating dispersion profile. The intensity of the inhomogeneous soliton can be controlled by means of modifying the loss/gain term. Asymptotic analysis of the two-soliton-like solution is performed, which shows that the changes of the widths, amplitudes, and energies before and after the collision are completely caused by the variable coefficients, but have nothing to do with the collision between two soliton-like envelopes. Through suitable choices of variable coefficients, figures are plotted to illustrate the collision behavior between two inhomogeneous solitons, which has some potential applications in the real optical communication systems.
KeywordsDerivative nonlinear Schrödinger equation with variable coefficients Lax pair Soliton-like solutions Symbolic computation
Unable to display preview. Download preview PDF.
- 10.Kivshar, S., Agrawal, G.P.: Optical Solitons: From Fibers to Photonic Crystals. Academic Press, San Diego (2003) Google Scholar
- 23.Mjølhus, E., Hada, T.: Soliton Theory of Quasi-parallel MHD Waves. In: Nonlinear Waves and Chaos in Space Plasmas. Terrapub, Tokyo (1997) Google Scholar
- 24.Abdullaev, F., Darmanyan, S., Khabibullaev, P.: Optical Solitons. Springer, Berlin (1991) Google Scholar
- 25.Agrawal, G.P.: Nonlinear Fiber Optics, 3rd edn. Academic Press, San Diego (2002) Google Scholar
- 26.Xu, T., Zhang, C.Y., Wei, G.M., Li, J., Meng, X.H., Tian, B.: Symbolic-computation construction of transformations for a more generalized nonlinear Schrödinger equation with applications in inhomogeneous plasmas, optical fibers, viscous fluids and Bose–Einstein condensates. Eur. Phys. J. B 55, 323–332 (2007) CrossRefGoogle Scholar
- 27.Xu, T., Li, J., Zhang, H.Q., Zhang, Y.X., Hu, W., Gao, Y.T., Tian, B.: Integrable aspects and applications of a generalized inhomogeneous N-coupled nonlinear Schrödinger system in plasmas and optical fibers via symbolic computation. Phys. Lett. A 372, 1990–2001 (2008) CrossRefMathSciNetGoogle Scholar