论文标题
耦合分散AB系统在低规律性空间中的长期渐近行为
Long-time Asymptotic Behavior of the coupled dispersive AB system in Low Regularity Spaces
论文作者
论文摘要
In this paper, we mainly investigate the long-time asymptotic behavior of the solution for the coupled dispersive AB system with weighted Sobolev initial data, which allows soliton solutions via the Dbar steepest descent method.Based on the spectral analysis of Lax pair, the Cauchy problem of the coupled dispersive AB system is transformed into a Riemann-Hilbert problem, and its existence and uniqueness of the solution is proved by the vanishing引理。固定相位点在长期渐近行为中起着重要作用。我们证明，在任何固定的时间锥$ \ mathcal {c} \ left（x_ {1}，x_ {2}，v_ {1}，v_ {2} \ right）= \ left \ left \ left \ {（x，x，x，x，x，x，t） \ in \左[x_ {1}，x_ {2} \ right]，v \ in \ left [v_ {1}，v_ {2} \ right] \ right \} $，可以通过$ n（\ n diars）表示coupled ab ab系统的长期渐近性分散式AB系统的解决方案的\ n（\ niv）。连续频谱上的订单项$ \ MATHCAL {O}（t^{ - 1 /2}）$和允许的残留$ \ MATHCAL {O}（T^{ - 3 /4}）$。
In this paper, we mainly investigate the long-time asymptotic behavior of the solution for the coupled dispersive AB system with weighted Sobolev initial data, which allows soliton solutions via the Dbar steepest descent method.Based on the spectral analysis of Lax pair, the Cauchy problem of the coupled dispersive AB system is transformed into a Riemann-Hilbert problem, and its existence and uniqueness of the solution is proved by the vanishing lemma. The stationary phase points play an important role in the long-time asymptotic behavior. We demonstrate that in any fixed time cone $\mathcal{C}\left(x_{1}, x_{2}, v_{1}, v_{2}\right)=\left\{(x, t) \in \mathbb{R}^{2} \mid x=x_{0}+v t, x_{0} \in\left[x_{1}, x_{2}\right], v \in\left[v_{1}, v_{2}\right]\right\}$, the long-time asymptotic behavior of the solution for the coupled dispersive AB system can be expressed by $N(\mathcal{I})$ solitons on the discrete spectrum, the leading order term $\mathcal{O}(t^{-1 / 2})$ on the continuous spectrum and the allowable residual $\mathcal{O}(t^{-3 / 4})$.
