Abstract
We study a deterministic gas of breathers for the Focusing Nonlinear Schrödinger equation. The gas of breathers
is obtained from a 𝑁-breather solution in the limit 𝑁 → ∞. 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 → ∞. 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 Bertola et al. (2023) for a soliton gas
also to a breather gas
is obtained from a 𝑁-breather solution in the limit 𝑁 → ∞. 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 → ∞. 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 Bertola et al. (2023) for a soliton gas
also to a breather gas
| Original language | English |
|---|---|
| Article number | 134744 |
| Number of pages | 11 |
| Journal | Physica D: Nonlinear Phenomena |
| Volume | 481 |
| Early online date | 29 May 2025 |
| DOIs | |
| Publication status | Published - 1 Nov 2025 |
Bibliographical note
Publisher Copyright:© 2025
Keywords
- Breather Shielding
- Nonlinear Schrodinger equation