Orbital Stability of Solitary Waves for the Nonlinear Derivative Schrödinger Equation

Consider herein are the stability of the solitary waves e−iωteiψ(x−vt)a(x−vt) for the following nonlinear quintic derivative Schrödinger equation. ut = iuxx + i(c3 u2 + c5 u4) u + [(s0 + s2 u2)u]x, u R. For the case s2 ≠ 0, the abstract results of Grillakis et al. [5, 6] do not apply directly. By constructing three appropriate invariants of motion and detailed spectral analysis, we obtain the stability of the solitary waves.