Abstract
Soliton solutions are studied for paraxial wave propagation with intensity-dependent dispersion. Although the corresponding Lagrangian density has a singularity, analytical solutions, derived by the pseudo-potential method and the corresponding phase diagram, exhibit one- and two-humped solitons with almost perfect agreement to numerical solutions. The results obtained in this work reveal a hitherto unexplored area of soliton physics associated with nonlinear corrections to wave dispersion.
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