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Abstract A class of symmetry transformations of a type originally introduced in a nonlinear optics context is used here to isolate an integrable Ermakov-Painlevé II reduction of a resonant NLS… Click to show full abstract
Abstract A class of symmetry transformations of a type originally introduced in a nonlinear optics context is used here to isolate an integrable Ermakov-Painlevé II reduction of a resonant NLS equation which encapsulates a nonlinear system in cold plasma physics descriptive of the uni-axial propagation of magneto-acoustic waves. A Bäcklund transformation is employed in the iterative generation of novel classes of solutions to the cold plasma system which involve either Yablonski-Vorob’ev polynomials or classical Airy functions.
Journal Title: Journal of Nonlinear Mathematical Physics
Year Published: 2018
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