Abstract
In the paper, the exact solutions to the cubic-quintic nonlinear Schrodinger equation with third and fourth-order dispersion terms is considered. The improved homogeneous balance method is used for constructing a series of new exact envelop wave solutions, including envelop solitary wave solutions, envelop periodic wave solutions and an envelop rational solution.
Highlights
IntroductionSince third and fourth-order dispersion terms play a crucially important role in describing the propagation of extremely short pulses, the generalized nonlinear Schrodinger equation iqz
Since third and fourth-order dispersion terms play a crucially important role in describing the propagation of extremely short pulses, the generalized nonlinear Schrodinger equation iqz − β2 2 qtt + γ1|q|2q =i β3 6 qttt β4 24 qtttt γ2|q|4q (1)is taken as a model for a sub-picoseconds pulse propagation in a medium which exhibits a parabolic nonlinearity law (Shundong, 2007, Karpman,1997)
The improved homogeneous balance method is used for constructing a series of new exact envelop wave solutions, including envelop solitary wave solutions, envelop periodic wave solutions and an envelop rational solution
Summary
Since third and fourth-order dispersion terms play a crucially important role in describing the propagation of extremely short pulses, the generalized nonlinear Schrodinger equation iqz. Q(z, t) is the slowly varying envelope of the electromagnetic field, β2 is the parameter of the group velocity dispersion, β3 and β4 are third-order and fourth-order dispersion, respectively, γ1 and γ2 are the nonlinearity coefficients (Karpman, 1998). As to this equation, its modulation instability of optical wave was numerically investigated (Woo-Pyo,2002), the relative exact analytic solutions were studied very few, the researchers mainly studied its several special cases because of itself complications.
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