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Propagating Wave Patterns in a Derivative Nonlinear Schrödinger System with Quintic Nonlinearity [article]

C. Rogers Australian Research Council Centre of Excellence for Mathematics & Statistics of Complex Systems, School of Mathematics, The University of New South Wales, Australia, Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Israel, Department of Mechanical Engineering, University of Hong Kong, Hong Kong)
2012 arXiv   pre-print

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Exact expressions are obtained for a diversity of propagating patterns for a derivative nonlinear Schr\"odinger equation with a quintic nonlinearity. These patterns include bright pulses, fronts and dark solitons. The evolution of the wave envelope is determined via a pair of integrals of motion, and reduction is achieved to Jacobi elliptic cn and dn function representations. Numerical simulations are performed to establish the existence of parameter ranges for stability. The derivative quintic
more » ... nonlinear Schr\"odinger model equations investigated here are important in the analysis of strong optical signals propagating in spatial or temporal waveguides.
arXiv:1207.2561v1 fatcat:r2h6ibvesvdupf3lndcw24qahq
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C. Rogers Australian Research Council Centre of Excellence for Mathematics & Statistics of Complex Systems, School of Mathematics, The University of New South Wales, Australia, Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Israel, Department of Mechanical Engineering, University of Hong Kong, Hong Kong). "Propagating Wave Patterns in a Derivative Nonlinear Schrödinger System with Quintic Nonlinearity." arXiv (2012)