Phys. Rev. E 67, 026603 (2003) [7 pages]Modulation instability and solitons on a cw background in an optical fiber with higher-order effectsReceived 5 August 2002; published 10 February 2003 We construct the Lax pair for a higher-order nonlinear Schrödinger equation that includes terms accounting for the third-order dispersion, the self-steepening effect, and the delayed nonlinear response effect. Two exact analytic solutions that describe (i) modulation instability and (ii) soliton propagation on a continuous wave background are obtained by using the Darboux transformation. In addition, we analyze the amplification-absorption and quintic nonlinearity effects on the second solution in the adiabatic approximation. © 2003 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.67.026603
DOI:
10.1103/PhysRevE.67.026603
PACS:
42.65.Tg, 42.81.Dp, 42.79.Sz
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