Ermakov-Painlevé II Reduction in Cold Plasma Physics. Application of a Bäcklund Transformation

A class of symmetry transformations of a type originally introduced in a nonlinear optics

context is used here to isolate an integrable Ermakov-Painlev´e II reduction of a resonant NLS

equation which encapsulates a nonlinear system in cold plasma physics descriptive of the uniaxial

propagation of magneto-acoustic waves. A B¨acklund 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