Orbital Stability of Solitary Waves for the Nonlinear Derivative Schrödinger Equation

Orbital stability of solitary waves for Kundu equation

“…Since Kundu equation is more complex than the derivative Schrödinger equation, we utilize some techniques to overcome some difficulties in this paper. It should be pointed out that the results obtained in this paper are more general than those obtained by Guo and Wu (1995). We present a sufficient condition under which solitary waves are orbitally stable for 2c 3 + s 2 υ < 0, while Guo and Wu (1995) only considered the case 2c 3 + s 2 υ > 0.…”

“…It should be pointed out that the results obtained in this paper are more general than those obtained by Guo and Wu (1995). We present a sufficient condition under which solitary waves are orbitally stable for 2c 3 + s 2 υ < 0, while Guo and Wu (1995) only considered the case 2c 3 + s 2 υ > 0. We obtain the results on orbital stability of solitary waves for the derivative Schrödinger equation given by Colin and Ohta (2006) as a corollary in this paper.…”

“…Furthermore, Guo and Wu proved that this kind of solitary waves for Eq. (2) are orbitally stable in [10]. For more results on Eq.…”

“…(1). Motivated by the approach in [10], we study this problem by constructing three appropriate invariants of motion and using detailed spectral analysis. Due to Eq.…”

“…The abstract orbital stability theory proposed by Grillakis et al (1987Grillakis et al ( , 1990) cannot be applied directly to study orbital stability of solitary waves for this equation. Motivated by the idea of Guo and Wu (1995), we construct three invariants of motion and use detailed spectral analysis to obtain orbital stability of solitary waves for Kundu equation. Since Kundu equation is more complex than the derivative Schrödinger equation, we utilize some techniques to overcome some difficulties in this paper.…”