General N-solitons and their dynamics in several nonlocal nonlinear Schrödinger equations
By Jianke Yang. Physics Letters, 2017
183 citations recorded by the source corpus.
General $N$-solitons in three recently-proposed nonlocal nonlinear Schr\"odinger equations are presented. These nonlocal equations include the reverse-space, reverse-time, and reverse-space-time nonlinear Schr\"odinger equations, which are nonlocal reductions of the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy. It is shown that general $N$-solitons in these different equations can be derived from the same Riemann-Hilbert solutions of the AKNS hierarchy, except that symmetry relations on the scattering data are different for these equations. This Riemann-Hilbert framework allows us to identify new types of solitons with novel eigenvalue configurations in the spectral plane. Dynamics of $N$-solitons in these equations is also explored. In all the three nonlocal equations, a generic feature of their solutions is repeated collapsing. In addition, multi-solitons can behave very differently from fundamental solitons and may not correspond to a nonlinear superposition of fundamental solitons.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/aacbae52b2e708e8f1efe9b7eb332e71f4bbb0cc
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In Atomic and Molecular Physics, and Optics
- Dmitry Shepelsky
- Yan Rybalko
- Xu‐Dan Luo
- B. Feng
- Ziad Musslimani
- Mark J. Ablowitz
- Jianke Yang
- Bo Yang
In Statistical and Nonlinear Physics
- Dmitry Shepelsky
- Yan Rybalko
- Xu‐Dan Luo
- B. Feng
- Ziad Musslimani
- Mark J. Ablowitz
- Jianke Yang
- Bo Yang
Citations in the corpus
- General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions (2017, methodology): “It is noted that all above four cases regarding the bright soliton solution to the nonlocal NLS equation have been recognized in [57], their dynamics and singularities have been discussed in details there.”
- Long-time asymptotics for the nonlocal nonlinear Schrödinger equation with step-like initial data (2021, background): “In [2] and [36], a general decaying N-soliton solution of (1.”