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  • 1
    Electronic Resource
    Electronic Resource
    Finite-dimensional integrable systems related to the n-wave interaction equations (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3554-3564 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Under a constraint between the potentials and the eigenfunctions, Lax pairs and adjoint Lax pairs of a soliton hierarchy associated with the n×n generalized Zakharov–Shabat eigenvalue problem are transformed into a spatial finite-dimensional Hamiltonian system and a hierarchy of temporal finite-dimensional Hamiltonian systems. The Lax representations, r-matrix structure and integrals of motion are explicitly presented. These integrals of motion are functionally independent and in involution in pairs, which shows that these systems, especially the whole hierarchy of temporal finite-dimensional Hamiltonian systems, are Liouville integrable. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1385565
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A finite-dimensional integrable system and the r-matrix method (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 2157-2166 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The nonlinearization method is used on the soliton hierarchy associated with the 4×4 AKNS eigenvalue problem, from which a new finite-dimensional Hamiltonian system is obtained by nonlinearization of the eigenvalue problem and its ajoint one. A Lax representation is deduced for the system. The Lax operator admits the representation of an r-matrix. The 4N functionally independent and involutive integrals of motion are obtained via the r-matrix, which shows that the system is completely integrable in the Liouville sense. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533232
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  • 3
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    Particle-in-cell simulation of the head-on collision between two ion acoustic solitary waves in plasmas (2014)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2014-08-30
    Description: The head-on collision of two ion acoustic solitary waves in plasmas composed of hot electrons and cold ions has been studied by using the Poincare-Lighthill-Kuo (PLK) perturbation method and one-dimensional Particle-in-Cell (PIC) simulation. Then the phase lags of ion acoustic solitary waves (IASWs) obtained from the two approaches have been compared and discussed. It has been found that: if the amplitudes of both the colliding IASWs are small enough, the phase lags obtained from PLK method are in good agreement with those obtained from PIC simulation. As the amplitudes of IASWs increase, the phase lags from PIC simulation become smaller than the analytical ones from PLK method. Besides, the PIC simulation shows the phase lag of an IASW involved in collision depends not only on the characteristics of the wave it collides with but also on itself, which disagrees with the prediction of the PLK method. Finally, the application scopes of the PLK method in studying both the single IASW and the head-on collisions of IASWs have been studied and discussed, and the latter turns out to be more strict.
    Print ISSN: 1070-664X
    Electronic ISSN: 1089-7674
    Topics: Physics
    Published by American Institute of Physics (AIP)
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