### Abstract

We address the breakup (splitting) of multisoliton solutions of the nonlinear Schrödinger equation (NLSE), occurring due to linear loss. Two different approaches are used for the study of the splitting process. The first one is based on the direct numerical solution of the linearly damped NLSE and the subsequent analysis of the eigenvalue drift for the associated Zakharov-Shabat spectral problem. The second one involves the multisoliton adiabatic perturbation theory applied for studying the evolution of the solution parameters, with the linear loss taken as a small perturbation. We demonstrate that in the case of strong nonadiabatic loss the evolution of the Zakharov-Shabat eigenvalues can be quite nontrivial. We also demonstrate that the multisoliton breakup can be correctly described within the framework of the adiabatic perturbation theory and can take place even due to small linear loss. Eventually we elucidate the occurrence of the splitting and its dependence on the phase mismatch between the solitons forming a two-soliton bound state.

Original language | English |
---|---|

Article number | 036616 |

Number of pages | 9 |

Journal | Physical Review E |

Volume | 75 |

Issue number | 3 |

DOIs | |

Publication status | Published - 28 Mar 2007 |

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### Bibliographical note

©2007 The American Physical Society. Breakup of a multisoliton state of the linearly damped nonlinear Schrödinger equationJaroslaw E. Prilepsky and Stanislav A. Derevyanko

Phys. Rev. E 75, 036616 – Published 28 March 2007

### Cite this

*Physical Review E*,

*75*(3), [036616]. https://doi.org/10.1103/PhysRevE.75.036616

}

*Physical Review E*, vol. 75, no. 3, 036616. https://doi.org/10.1103/PhysRevE.75.036616

**Breakup of a multisoliton state of the linearly damped nonlinear Schrödinger equation.** / Prilepsky, Jaroslaw E.; Derevyanko, Stanislav A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Breakup of a multisoliton state of the linearly damped nonlinear Schrödinger equation

AU - Prilepsky, Jaroslaw E.

AU - Derevyanko, Stanislav A.

N1 - ©2007 The American Physical Society. Breakup of a multisoliton state of the linearly damped nonlinear Schrödinger equation Jaroslaw E. Prilepsky and Stanislav A. Derevyanko Phys. Rev. E 75, 036616 – Published 28 March 2007

PY - 2007/3/28

Y1 - 2007/3/28

N2 - We address the breakup (splitting) of multisoliton solutions of the nonlinear Schrödinger equation (NLSE), occurring due to linear loss. Two different approaches are used for the study of the splitting process. The first one is based on the direct numerical solution of the linearly damped NLSE and the subsequent analysis of the eigenvalue drift for the associated Zakharov-Shabat spectral problem. The second one involves the multisoliton adiabatic perturbation theory applied for studying the evolution of the solution parameters, with the linear loss taken as a small perturbation. We demonstrate that in the case of strong nonadiabatic loss the evolution of the Zakharov-Shabat eigenvalues can be quite nontrivial. We also demonstrate that the multisoliton breakup can be correctly described within the framework of the adiabatic perturbation theory and can take place even due to small linear loss. Eventually we elucidate the occurrence of the splitting and its dependence on the phase mismatch between the solitons forming a two-soliton bound state.

AB - We address the breakup (splitting) of multisoliton solutions of the nonlinear Schrödinger equation (NLSE), occurring due to linear loss. Two different approaches are used for the study of the splitting process. The first one is based on the direct numerical solution of the linearly damped NLSE and the subsequent analysis of the eigenvalue drift for the associated Zakharov-Shabat spectral problem. The second one involves the multisoliton adiabatic perturbation theory applied for studying the evolution of the solution parameters, with the linear loss taken as a small perturbation. We demonstrate that in the case of strong nonadiabatic loss the evolution of the Zakharov-Shabat eigenvalues can be quite nontrivial. We also demonstrate that the multisoliton breakup can be correctly described within the framework of the adiabatic perturbation theory and can take place even due to small linear loss. Eventually we elucidate the occurrence of the splitting and its dependence on the phase mismatch between the solitons forming a two-soliton bound state.

UR - http://www.scopus.com/inward/record.url?scp=33947729831&partnerID=8YFLogxK

UR - http://journals.aps.org/pre/abstract/10.1103/PhysRevE.75.036616

U2 - 10.1103/PhysRevE.75.036616

DO - 10.1103/PhysRevE.75.036616

M3 - Article

AN - SCOPUS:33947729831

VL - 75

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 3

M1 - 036616

ER -