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Abstract Up to the third-order rogue wave solutions of the Sasa–Satsuma (SS) equation are derived based on the Hirota’s bilinear method and Kadomtsev–Petviashvili hierarchy reduction method. They are expressed explicitly by rational functions with both the numerator and denominator being the determinants of even order. Four types of intrinsic structures are recognized according to the number of zero-amplitude points. The first- and second-order rogue wave solutions agree with the solutions obtained so far by the Darboux transformation. In spite of the very complicated solution form compared with the ones of many other integrable equations, the third-order rogue waves exhibit two configurations: either a triangle or a distorted pentagon. Both the types and configurations of the third-order rogue waves are determined by different choices of free parameters. As the nonlinear Schrödinger equation is a limiting case of the SS equation, it is shown that the degeneration of the first-order rogue wave of the SS equation converges to the Peregrine soliton.
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Relation between solutions of the Schrödinger equation with transitioning resonance solutions of the gravitational three-body problem
Abstract It is shown that a class of approximate resonance solutions in the three-body problem under the Newtonian gravitational force are equivalent to quantized solutions of a modified Schrödinger equation for a wide range of masses that transition between energy states. In the macroscopic scale, the resonance solutions are shown to transition from one resonance type to another through weak capture at one of the bodies, while in the Schrödinger equation, one obtains quantized wave solutions transitioning between different energies. The resonance transition dynamics provides a classical model of a particle moving between different energy states in the Schrödinger equation. This methodology provides a connection between celestial and quantum mechanics.
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- Award ID(s):
- 1814543
- PAR ID:
- 10302745
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Journal of Physics Communications
- Volume:
- 4
- Issue:
- 1
- ISSN:
- 2399-6528
- Page Range / eLocation ID:
- Article No. 015012
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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