Theoretical modeling demonstrates exact bright solitons and cnoidal waves under second-order spatiotemporal dispersion, indicating conventional pulse theory arises as a limiting regime.
We propose a simple scalar model for describing pulse phenomena beyond the conventional slowly varying envelope approximation. The generic governing equation has a cubic nonlinearity, and we focus here mainly on contexts involving anomalous group-velocity dispersion. Pulse propagation turns out to be a problem firmly rooted in frames-of-reference considerations. The transformation properties of the model and its space-time structure are explored in detail. Two distinct representations of exact analytical solitons and their associated conservation laws (in both integral and algebraic forms) are presented, and a range of predictions is made. We also report cnoidal waves of the governing nonlinear equation. Crucially, conventional pulse theory is shown to emerge as a limit of the more general formulation. Extensive simulations examine the role of the new solitons as robust attractors.
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Christian et al. (2012) studied this question.
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