Articles | Volume 14, issue 6
https://doi.org/10.5194/nhess-14-1431-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Special issue:
https://doi.org/10.5194/nhess-14-1431-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
06 Jun 2014
Research article |
| 06 Jun 2014
Numerical investigation of stability of breather-type solutions of the nonlinear Schrödinger equation
A. Calini
Department of Mathematics, College of Charleston, Charleston, SC, USA
C. M. Schober
Department of Mathematics, University of Central Florida, Orlando, FL, USA
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Cited
19 citations as recorded by crossref.
- The routes to stability of spatially periodic solutions of the linearly damped NLS equation C. Schober & A. Islas https://doi.org/10.1140/epjp/s13360-020-00660-w
- Numerical investigation of the stability of the rational solutions of the nonlinear Schrödinger equation A. Islas & C. Schober https://doi.org/10.1016/j.amc.2017.01.060
- The linear and nonlinear instability of the Akhmediev breather P. Grinevich & P. Santini https://doi.org/10.1088/1361-6544/ac3143
- New coupled rogue waves propagating backward and forward and modulation instability in a composite nonlinear right- and left-handed transmission line D. Ahmadou et al. https://doi.org/10.1140/epjp/s13360-021-02054-y
- Peregrine Solitons of the Higher-Order, Inhomogeneous, Coupled, Discrete, and Nonlocal Nonlinear Schrödinger Equations T. Uthayakumar et al. https://doi.org/10.3389/fphy.2020.596886
- Breather dynamics in a stochastic sine-Gordon equation: Evidence of noise-enhanced stability D. De Santis et al. https://doi.org/10.1016/j.chaos.2023.113115
- Riemann Surfaces Close to Degenerate Ones in the Theory of Rogue Waves P. Grinevich https://doi.org/10.1134/S0081543824020056
- Darboux Transformation of the Second-Type Derivative Nonlinear Schrödinger Equation Y. Zhang et al. https://doi.org/10.1007/s11005-015-0758-x
- Multi-breather asymptotics for a nonlinear Schrödinger equation arising in oceanography, plasma physics, Bose–Einstein condensation and fiber optics X. Wu & Y. Gao https://doi.org/10.1016/j.matcom.2025.03.018
- Breather and rogue wave solutions for a nonlinear Schrödinger-type system in plasmas G. Meng et al. https://doi.org/10.1007/s11071-015-2024-2
- Adiabatic transformation of continuous waves into trains of pulses J. Soto-Crespo et al. https://doi.org/10.1103/PhysRevA.96.023825
- Multidomain spectral method for Schrödinger equations M. Birem & C. Klein https://doi.org/10.1007/s10444-015-9429-9
- Breather solutions of a fourth-order nonlinear Schrödinger equation in the degenerate, soliton, and rogue wave limits A. Chowdury et al. https://doi.org/10.1103/PhysRevE.96.042209
- Nonlinear damped spatially periodic breathers and the emergence of soliton-like rogue waves C. Schober & A. Islas https://doi.org/10.1016/j.physd.2022.133356
- Floquet analysis of Kuznetsov-Ma breathers: A path towards spectral stability of rogue waves J. Cuevas-Maraver et al. https://doi.org/10.1103/PhysRevE.96.012202
- Ac-locking of thermally-induced sine-Gordon breathers D. De Santis et al. https://doi.org/10.1016/j.chaos.2023.113382
- On the Stabilization of Breather-type Solutions of the Damped Higher Order Nonlinear Schrödinger Equation C. Schober & A. Islas https://doi.org/10.3389/fphy.2021.633890
- Localized modes of the Hirota equation: Nth order rogue wave and a separation of variable technique G. Mu et al. https://doi.org/10.1016/j.cnsns.2016.02.028
- Linear instability of the Peregrine breather: Numerical and analytical investigations A. Calini et al. https://doi.org/10.1016/j.apnum.2018.11.005
19 citations as recorded by crossref.
- The routes to stability of spatially periodic solutions of the linearly damped NLS equation C. Schober & A. Islas https://doi.org/10.1140/epjp/s13360-020-00660-w
- Numerical investigation of the stability of the rational solutions of the nonlinear Schrödinger equation A. Islas & C. Schober https://doi.org/10.1016/j.amc.2017.01.060
- The linear and nonlinear instability of the Akhmediev breather P. Grinevich & P. Santini https://doi.org/10.1088/1361-6544/ac3143
- New coupled rogue waves propagating backward and forward and modulation instability in a composite nonlinear right- and left-handed transmission line D. Ahmadou et al. https://doi.org/10.1140/epjp/s13360-021-02054-y
- Peregrine Solitons of the Higher-Order, Inhomogeneous, Coupled, Discrete, and Nonlocal Nonlinear Schrödinger Equations T. Uthayakumar et al. https://doi.org/10.3389/fphy.2020.596886
- Breather dynamics in a stochastic sine-Gordon equation: Evidence of noise-enhanced stability D. De Santis et al. https://doi.org/10.1016/j.chaos.2023.113115
- Riemann Surfaces Close to Degenerate Ones in the Theory of Rogue Waves P. Grinevich https://doi.org/10.1134/S0081543824020056
- Darboux Transformation of the Second-Type Derivative Nonlinear Schrödinger Equation Y. Zhang et al. https://doi.org/10.1007/s11005-015-0758-x
- Multi-breather asymptotics for a nonlinear Schrödinger equation arising in oceanography, plasma physics, Bose–Einstein condensation and fiber optics X. Wu & Y. Gao https://doi.org/10.1016/j.matcom.2025.03.018
- Breather and rogue wave solutions for a nonlinear Schrödinger-type system in plasmas G. Meng et al. https://doi.org/10.1007/s11071-015-2024-2
- Adiabatic transformation of continuous waves into trains of pulses J. Soto-Crespo et al. https://doi.org/10.1103/PhysRevA.96.023825
- Multidomain spectral method for Schrödinger equations M. Birem & C. Klein https://doi.org/10.1007/s10444-015-9429-9
- Breather solutions of a fourth-order nonlinear Schrödinger equation in the degenerate, soliton, and rogue wave limits A. Chowdury et al. https://doi.org/10.1103/PhysRevE.96.042209
- Nonlinear damped spatially periodic breathers and the emergence of soliton-like rogue waves C. Schober & A. Islas https://doi.org/10.1016/j.physd.2022.133356
- Floquet analysis of Kuznetsov-Ma breathers: A path towards spectral stability of rogue waves J. Cuevas-Maraver et al. https://doi.org/10.1103/PhysRevE.96.012202
- Ac-locking of thermally-induced sine-Gordon breathers D. De Santis et al. https://doi.org/10.1016/j.chaos.2023.113382
- On the Stabilization of Breather-type Solutions of the Damped Higher Order Nonlinear Schrödinger Equation C. Schober & A. Islas https://doi.org/10.3389/fphy.2021.633890
- Localized modes of the Hirota equation: Nth order rogue wave and a separation of variable technique G. Mu et al. https://doi.org/10.1016/j.cnsns.2016.02.028
- Linear instability of the Peregrine breather: Numerical and analytical investigations A. Calini et al. https://doi.org/10.1016/j.apnum.2018.11.005
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