### Abstract

We show, in general, how to transform the nonautonomous nonlinear Schrödinger equation with quadratic Hamiltonians into the standard autonomous form that is completely integrable by the familiar inverse scattering method in nonlinear science. Derivation of the corresponding equivalent nonisospectral Lax pair is also outlined. A few simple integrable systems are discussed.

Original language | English (US) |
---|---|

Pages (from-to) | 3067-3082 |

Number of pages | 16 |

Journal | Proceedings of the American Mathematical Society |

Volume | 140 |

Issue number | 9 |

DOIs | |

State | Published - Sep 2012 |

### Fingerprint

### Keywords

- Completely integrable systems
- Generalized harmonic oscillators
- Green's function
- Lax pair
- Nonlinear Schrödinger equations
- Propagator
- Zakharov-Shabat system

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**On integrability of nonautonomous nonlinear schrödinger equations.** / Suslov, Sergei.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 140, no. 9, pp. 3067-3082. https://doi.org/10.1090/S0002-9939-2011-11176-6

}

TY - JOUR

T1 - On integrability of nonautonomous nonlinear schrödinger equations

AU - Suslov, Sergei

PY - 2012/9

Y1 - 2012/9

N2 - We show, in general, how to transform the nonautonomous nonlinear Schrödinger equation with quadratic Hamiltonians into the standard autonomous form that is completely integrable by the familiar inverse scattering method in nonlinear science. Derivation of the corresponding equivalent nonisospectral Lax pair is also outlined. A few simple integrable systems are discussed.

AB - We show, in general, how to transform the nonautonomous nonlinear Schrödinger equation with quadratic Hamiltonians into the standard autonomous form that is completely integrable by the familiar inverse scattering method in nonlinear science. Derivation of the corresponding equivalent nonisospectral Lax pair is also outlined. A few simple integrable systems are discussed.

KW - Completely integrable systems

KW - Generalized harmonic oscillators

KW - Green's function

KW - Lax pair

KW - Nonlinear Schrödinger equations

KW - Propagator

KW - Zakharov-Shabat system

UR - http://www.scopus.com/inward/record.url?scp=84861367006&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861367006&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2011-11176-6

DO - 10.1090/S0002-9939-2011-11176-6

M3 - Article

AN - SCOPUS:84861367006

VL - 140

SP - 3067

EP - 3082

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 9

ER -