Chirped bright and dark solitons of (3 + 1)-dimensional coupled nonlinear Schrödinger equations in negative-index metamaterials with both electric and magnetic nonlinearity of Kerr type
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The (3 + 1)-dimensional generalized coupled nonlinear Schrödinger equation with electric and magnetic nonlinearities of Kerr type and self-steepening effects is studied, and bright and dark soliton solutions are derived. Based on these analytical solutions, dynamical behaviors of bright and dark solitons are discussed. The amplitudes, widths and velocities of bright and dark solitons are all constants determined by the self-steepening effect parameters SE, SH. The phase chirp of a bright soliton diminishes in the pulse front of y-direction, however, it increases in the pulse back edge of y-direction. On the contrary, the phase chirp of a dark soliton increases in the pulse front of y-direction, however, it diminishes in the pulse back edge of y-direction. The phase chirps of a bright and dark soliton both shift along positive y -axis as time goes on. Moreover, the stability of the solutions is discussed.
- 4.C. Caloz, T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications (Wiley Interscience, 2006)Google Scholar