Stability Analysis and Conservation Laws via Multiplier Approach for the Perturbed Kaup-Newell Equation

Abstract

This paper presents the stability analysis (SA) and the conservation laws (Cls) for the perturbed Kaup-Newell equation (pKNE) by using the stability analysis technique and the multiplier method, respectively. The pKNE was recently introduced from a generalized Kaup-Newell spectral problem with linear perturbation with an arbitrary constant beta. In a situation where by beta = 0 one reaches the standard Kaup-Newell equation which possesses a tri-Hamiltonian feature and is the Euler-Poincare flow on the space of first order differential operator.