Localized and periodic wave patterns for a nonic nonlinear Schrödinger equation |
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| Authors: | Kwok W. Chow Colin Rogers |
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| Affiliation: | 1. Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong;2. Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems, School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia |
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| Abstract: | Propagating modes in a class of ‘nonic’ derivative nonlinear Schrödinger equations incorporating ninth order nonlinearity are investigated by application of two key invariants of motion. A nonlinear equation for the squared wave amplitude is derived thereby which allows the exact representation of periodic patterns as well as localized bright and dark pulses in terms of elliptic and their classical hyperbolic limits. These modes represent a balance among cubic, quintic and nonic nonlinearities. |
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| Keywords: | Nonlinear Schrö dinger equations Ninth order nonlinearity |
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