Noether Symmetries of the Triple Degenerate DNLS Equations

In this paper, Lie symmetries and Noether symmetries along with the corresponding conservation laws are derived for weakly nonlinear dispersive magnetohydrodynamic wave equations, also known as the triple degenerate derivative nonlinear Schr & ouml;dinger equations. The main goal of this study is to obtain Noether symmetries of the second-order Lagrangian density for these equations using the Noether symmetry approach with a gauge term. For this Lagrangian density, we compute the conserved densities and fluxes corresponding to the Noether symmetries with a gauge term, which differ from the conserved densities obtained using Lie symmetries in Webb et al. (J. Plasma Phys. 1995, 54, 201-244; J. Phys. A Math. Gen. 1996, 29, 5209-5240). Furthermore, we find some new Lie symmetries of the dispersive triple degenerate derivative nonlinear Schr & ouml;dinger equations for non-vanishing integration functions Ki(t) (i=1,2,3).