Abstract
A generalized nonlinear Schrodinger equation with higher-order dispersive and nonlinear effects is presented to govern the pulse propagation in negative index materials. Via the mapping method, Jacobian elliptic function solutions and their corresponding soliton solutions are found. Parameter modulation of higher-order dispersive effect and nonlinearities for periodic waves and solitons is studied. With the addition of the third dispersion parameter, or the quintic nonlinear parameter, the change of real and imaginary parts of periodic waves and solitons is same; namely, their amplitudes increase, and yet their widths decrease. Moreover, phase transitions of solutions with parameter modulation are found.
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