Abstract
A variational method is used to derive stationary solutions of the generalized nonlinear Schrödinger equation with complex coefficients that describes growth and damping which has been introduced and solved in the 1 + 1 dimensional case by Pereira and Stenflo (1977 Phys. Fluids 20 1733). In the 1+1 dimensional case, the exact classical Pereira-Stenflo soliton solution is reproduced. Application to the 1 + 2 dimensional case with cylindrical symmetry, provides an explicit approximate single soliton solution which is named the cylindrical Pereira-Stenflo soliton.
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