Abstract
Starting from a simple dispersion relation for negative index materials and a heuristic nonlinear Klein-Gordon-type extension, we derive the evolution equations for the envelopes of beams and spatiotemporal pulses in nonlinear dispersive negative index media. Using existing numerical methods, based on fast Fourier-Bessel transforms, we study the stability of the solitary wave solutions. Nonlinearity and dispersion management are then incorporated to find stable solutions of the underlying partial differential equations.
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