In the current issue, we consider two coupled weakly dissipative fractional Schrödinger equations with cubic nonlinearities that reads\[\begin{cases}u_t - i(-\Delta)^{\frac{\alpha}{2}} u + i ({\lvert u \rvert}^2 + {\lvert v \rvert}^2) u + \gamma u = f \\v_t - i(-\Delta)^{\frac{\alpha}{2}} v + i ({\lvert u \rvert}^2 + {\lvert v \rvert}^2) v + \delta v_x + \gamma v = g\end{cases}\]We will prove that the asymptotic dynamics of the solutions will be described by the existence of a regular compact global attractor in the phase space with finite fractal dimension.

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一类二元非线性分数阶Schrödinger方程解的渐近行为

在当前问题中，我们考虑具有立方非线性的两个耦合的弱耗散分数薛定ding方程，其读为\ [\\ begin {cases} u_t-i（-\ Delta）^ {\ frac {\ alpha} {2}} u + i（ {\ lvert u \ rvert} ^ 2 + {\ lvert v \ rvert} ^ 2）u + \ gamma u = f \\ v_t-i（-\ Delta）^ {\ frac {\ alpha} {2}} v + i（{\ lvert u \ rvert} ^ 2 + {\ lvert v \ rvert} ^ 2）v + \ delta v_x + \ gamma v = g \ end {cases} \]我们将证明解决方案将通过在有限分形维数的相空间中存在规则的致密整体吸引子来描述。