Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation

On the Global Well-Posedness and Orbital Stability of Standing Waves for the Schrödinger Equation with Fractional Dissipation

“…Li and Zheng et al proved orbital stability of periodic standing waves for the coupled Klein-Gordon-Zakharov equations in [17]. There are other results of global well-posedness and stability of standing waves, such as the derivative nonlinear Schrödinger equation [18], the Moser-Trudinger type Schrödinger equation with fractional dissipation [19], the cubic fractional nonlinear Schrödinger equation [20], the logarithmic Klein-Gordon Equation [21], and so on. For the recent related studies of the fractional Schrödinger equation, we can refer to the works about dissipative character of asymptotics [22], the large time asymptotic behavior of solutions [23], blow-up criteria and instability of normalized standing waves [24], bound state solutions [25], the classification of single traveling wave solutions [26], and so on.…”