A perturbation theory for Alfvén solitons
A perturbation method for the perturbed DNLS-equation \[ (1)\quad q_ t+\{| q|^ 2q\}_ x+iq_{xx}=\sigma Q_ 1[q],\quad 0<\sigma <<1 \] is presented, where \(Q_ 1[q]=q_{xx}\). By using the inverse scattering transform which has been obtained in the paper of \textit{D. J. Kaup} and \textit{. A. C. Newell} [J. Math. Phys. 19, 798-801 (1978; Zbl 0383.35015)] for equation (1) as \(\sigma =0\), the authors obtained the correspondence between Alfvén solitons and eigenvalues for the perturbed DNLS equation (1), and discuss some properties of Alfvén solitons.
derivative nonlinear Schrödinger equation
scientific article; zbMATH DE number 3957744
scientific article