Multi-soliton complexes. (English) Zbl 1020.35101
Bona, Jerry (ed.) et al., The legacy of the inverse scattering transform in applied mathematics. Proceedings of an AMS-IMS-SIAM joint summer research conference, South Hadley, MA, USA, June 17-21, 2001. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 301, 117-138 (2002).
Summary: This paper reviews the latest advances in the area of multi-soliton complexes (MSCs). We present exact analytical solutions of coupled nonlinear Schrödinger equations, which describe multi-soliton complexes and their interactions on top of a background in media with self-focusing or self-defocusing Kerr-like nonlinearities. We present numerical examples illustrating the remarkable properties of MSCs, such as their reshaping after collisions. This occurs because the fundamental solitons composing an MSC can acquire different lateral shifts.
We also obtain an accurate estimate for the peak intensities of stationary and interacting MSCs, by establishing a rigorous relationship between the eigenvalues of incoherently-coupled fundamental solitons and the range of admissible intensities.
For the entire collection see [Zbl 1001.00024].
We also obtain an accurate estimate for the peak intensities of stationary and interacting MSCs, by establishing a rigorous relationship between the eigenvalues of incoherently-coupled fundamental solitons and the range of admissible intensities.
For the entire collection see [Zbl 1001.00024].
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 37K15 | Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems |
| 35Q51 | Soliton equations |
