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) |
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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 |
Keywords
- Completely integrable systems
- Generalized harmonic oscillators
- Green's function
- Lax pair
- Nonlinear Schrödinger equations
- Propagator
- Zakharov-Shabat system
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics