From nonlinear Schroedinger hierarchy to some (2+1)-dimensional nonlinear pseudodifferential equations

Journal Article · Sun Aug 15 00:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3453389· OSTI ID:21476543

Xiao, Yang; Dianlou, Du ^[1]

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1. Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450002 (China)

The Poisson structure on C{sup N}xR{sup N} is introduced to give the Hamiltonian system associated with a spectral problem which yields the nonlinear Schroedinger (NLS) hierarchy. The Hamiltonian system is proven to be Liouville integrable. Some (2+1)-dimensional equations including NLS equation, Kadomtesev-Petviashvili I (KPI) equation, coupled KPI equation, and modified Kadomtesev-Petviashvili (mKP) equation, are decomposed into Hamilton flows via the NLS hierarchy. The algebraic curve, Abel-Jacobi coordinates, and Riemann-Jacobi inversion are used to obtain the algebrogeometric solutions of these equations.

• OSTI ID: 21476543
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 8; Other Information: DOI: 10.1063/1.3453389; (c) 2010 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

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QUANTUM MECHANICS
SCHROEDINGER EQUATION
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