Envelope solutions to nonlinear Schr?dinger equation

Abstract

F-expansion method proposed recently is extended to construct more exact solutio ns of nonlinear evolution equations. To be more precise, it means that instead o f the first-order ordinary differential equation(ODE) and finite power series of one variable in F-expansion met hod, we introduce similar first-order ODEs and finite power series of two varia b les, each one of which is the component of solution to ODEs. As an illust rat ive example, using this extended F-expansion method we solve nonlinear Schrdin g er(NLS) equation, an abundance of envelope solutions, especially the solutions expressed by two different Jacobi elliptic functions, to the NLS equation have b een obtai ned. Obviously, the extended F-expansion method can be applied to solve other ty pe of nonlinear evolution equations as well.