Explicit and implicit solutions for the one-dimensional cubic and quintic complex Ginzburg–Landau equations

In this work the one-dimensional cubic and quintic complex Ginzburg–Landau equations (CGL) are investigated. Generalized forms of these equations with nonlinearity of order (2n+1)(2n+1) and (4n+1)(4n+1) are examined as well. Explicit and implicit solutions are formally derived.