标题： 聚焦非线性薛定谔方程中呼吸子的屏蔽 显示英文标题

标题： Shielding of breathers for the focusing nonlinear Schrödinger equation

摘要： 我们研究聚焦非线性薛定谔方程的确定性孤子气体。 孤子气体是从$N$-孤子解在极限$N\to \infty$下得到的。\\ 该极限是在散射数据层面进行的，通过让$N$-孤子谱在极限$N\to\infty$下均匀地填满复平面上一个合适的紧致区域。 相应的归一化常数由一个光滑函数插值并按$1/N$进行缩放。 对于特定的区域和插值函数的选择，孤子气体表现出有限孤子解的行为。 这扩展了在“M. Bertola, T. Grava, and G. Orsatti - Physical Review Letters, 130.12 (2023): 1”中发现的对于孤子气体的屏蔽效应，也适用于孤子气体。 显示英文摘要

摘要： We study a deterministic gas of breathers for the Focusing Nonlinear Schr\"odinger equation. The gas of breathers is obtained from a $N$-breather solution in the limit $N\to \infty$.\\ The limit is performed at the level of scattering data by letting the $N$-breather spectrum to fill uniformly a suitable compact domain of the complex plane in the limit $N\to\infty$. The corresponding norming constants are interpolated by a smooth function and scaled as $1/N$. For particular choices of the domain and the interpolating function, the gas of breathers behaves as finite breathers solution. This extends the shielding effect discovered in "M. Bertola, T. Grava, and G. Orsatti - Physical Review Letters, 130.12 (2023): 1" for a soliton gas also to a breather gas.