Abstract
In this letter, the generalized nonlinear Schrodinger (GNLS) equation, phase-locked a source κ ei[χ(ξ)−ωt]: , is investigated. Firstly, we reduce this equation to a second-order non-homogeneous nonlinear ordinary differential equation via a plane wave transformation and some constraint conditions. Then we use some fractional transformations to study exact solutions in obtaining the GNLS equation. As a consequence, many types of exact solutions are deduced such as envelope rational solutions, envelope periodic wave solutions, envelope solitary wave solutions and envelope doubly periodic solutions. Similarly, the corresponding exact solutions can also be obtained for the Hirota-type GNLS equation with a source and their combined equation.
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