OPTICAL SOLITARY WAVES FOR THE GENERALIZED HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION WITH VARIABLE COEFFICIENTS

In this paper, four kinds of optical solitary wave solutions, including bright, dark optical solitary waves and new types of solitary waves (W-shaped and M-shaped), for the generalized higher-order nonlinear Schrödinger equation (GHONLSE) with variable coefficients are considered under certain parametric conditions. Among these solutions, the W-shaped and M-shaped solitary waves, which cannot exist in the variable-coefficient nonlinear Schrödinger equation (vNLSE), are first given for the GHONLSE with variable coefficients. As examples, we analyze the properties of these solitary wave solutions in some periodic distributed amplification systems. When α₁(z)=0, these bright and dark optical solitary wave solutions agree with the corresponding solutions in Refs. 25, 26 and 27, and the W-shaped solitary wave is in agreement with the corresponding result in Ref. 29. When α₃(z)–α₇(z) are constants and α₁(z)=α₂(z)=0, the W-shaped and M-shaped solitary waves in Refs. 14 and 15 can be recovered, respectively. Under the absence of the higher-order terms (α₄(z), α₆(z), α₇(z)) and α₁(z)=0, we provide the same results as reported in Refs. 22 and 23. This means that our results have more general forms than the earlier reports.