Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 043518 |
| Fachzeitschrift | Physical Review A |
| Jahrgang | 110 |
| Ausgabenummer | 4 |
| Publikationsstatus | Veröffentlicht - 22 Okt. 2024 |
Abstract
We numerically study solitary-wave solutions for the nonlinear Schrödinger equation perturbed by the effects of third-order and negative fourth-order dispersion. At a single wave number, an analytical expression for a localized solution with nonzero velocity, here referred to as Kruglov and Harvey's solitary-wave solution, is known to exist. To obtain solitary waves for general wave numbers and velocities, we employ a custom spectral renormalization method. For a selected set of system parameters and a range of wave numbers, we characterize the resulting pulses via a fit model, allowing us to formulate empirical relations between the pulse parameters. Deeper insight into the interaction dynamics of these solitary waves can be obtained through collisions. These collisions are typically inelastic and allow for the formation of short-lived two-pulse bound states with very particular dynamics. Finally, we detail the properties of Kruglov and Harvey's soliton solution under weak loss. For short propagation distances our numerical results verify earlier predictions of perturbation theory and show that the pulse shape is altered upon propagation. For long distances we observe a crossover to linear pulse broadening.
ASJC Scopus Sachgebiete
- Physik und Astronomie (insg.)
- Atom- und Molekularphysik sowie Optik
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in: Physical Review A, Jahrgang 110, Nr. 4, 043518, 22.10.2024.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Numerical investigation of solitary-wave solutions for the nonlinear Schrödinger equation perturbed by third-order and negative fourth-order dispersion
AU - Melchert, Oliver
AU - Demircan, Ayhan
N1 - Publisher Copyright: © 2024 American Physical Society.
PY - 2024/10/22
Y1 - 2024/10/22
N2 - We numerically study solitary-wave solutions for the nonlinear Schrödinger equation perturbed by the effects of third-order and negative fourth-order dispersion. At a single wave number, an analytical expression for a localized solution with nonzero velocity, here referred to as Kruglov and Harvey's solitary-wave solution, is known to exist. To obtain solitary waves for general wave numbers and velocities, we employ a custom spectral renormalization method. For a selected set of system parameters and a range of wave numbers, we characterize the resulting pulses via a fit model, allowing us to formulate empirical relations between the pulse parameters. Deeper insight into the interaction dynamics of these solitary waves can be obtained through collisions. These collisions are typically inelastic and allow for the formation of short-lived two-pulse bound states with very particular dynamics. Finally, we detail the properties of Kruglov and Harvey's soliton solution under weak loss. For short propagation distances our numerical results verify earlier predictions of perturbation theory and show that the pulse shape is altered upon propagation. For long distances we observe a crossover to linear pulse broadening.
AB - We numerically study solitary-wave solutions for the nonlinear Schrödinger equation perturbed by the effects of third-order and negative fourth-order dispersion. At a single wave number, an analytical expression for a localized solution with nonzero velocity, here referred to as Kruglov and Harvey's solitary-wave solution, is known to exist. To obtain solitary waves for general wave numbers and velocities, we employ a custom spectral renormalization method. For a selected set of system parameters and a range of wave numbers, we characterize the resulting pulses via a fit model, allowing us to formulate empirical relations between the pulse parameters. Deeper insight into the interaction dynamics of these solitary waves can be obtained through collisions. These collisions are typically inelastic and allow for the formation of short-lived two-pulse bound states with very particular dynamics. Finally, we detail the properties of Kruglov and Harvey's soliton solution under weak loss. For short propagation distances our numerical results verify earlier predictions of perturbation theory and show that the pulse shape is altered upon propagation. For long distances we observe a crossover to linear pulse broadening.
UR - http://www.scopus.com/inward/record.url?scp=85207422556&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.110.043518
DO - 10.1103/PhysRevA.110.043518
M3 - Article
AN - SCOPUS:85207422556
VL - 110
JO - Physical Review A
JF - Physical Review A
SN - 2469-9926
IS - 4
M1 - 043518
ER -