Open AccessEnvelope solutions to nonlinear Schr?dinger equation
Author(s) -
Xiangzheng Li,
Jinliang Zhang,
Yueming Wang,
Mingliang Wang
Publication year - 2004
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.53.4045
Subject(s) - ode , power series , envelope (radar) , nonlinear system , ordinary differential equation , series (stratigraphy) , mathematical analysis , physics , asymptotic expansion , differential equation , mathematical physics , mathematics , quantum mechanics , computer science , biology , telecommunications , radar , paleontology
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 Schrdin 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.