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  • 1
    Electronic Resource
    Electronic Resource
    On relative invariants (1997)
    Springer
    Mathematische Annalen 308 (1997), S. 701-732 
    Details
    ISSN: 1432-1807
    Keywords: Mathematics Subject Classification (1991): 13A50 ; 14D25 ; 22E45 ; 53C05 ; 54H15 ; 58D15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002080050097
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  • 2
    Electronic Resource
    Electronic Resource
    Multi-Hamiltonian structure of the Born–Infeld equation (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1338-1344 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The multi-Hamiltonian structure, conservation laws, and higher order symmetries for the Born–Infeld equation are exhibited. A new transformation of the Born-Infeld equation to the equations of a Chaplygin gas is presented and explored. The Born–Infeld equation is distinguished among two-dimensional hyperbolic systems by its wealth of such multi-Hamiltonian structures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528314
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  • 3
    Electronic Resource
    Electronic Resource
    Quantization of bi-Hamiltonian systems (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 113-117 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: One of the distinguishing features of soliton equations is the fact that they can be written in Hamiltonian form in more than one way. Here we compare the different quantized versions of the soliton equations arising in the AKNS inverse scattering scheme. It is found that, when expressed in terms of the scattering data, both quantized versions are essentially identical.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528868
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  • 4
    Electronic Resource
    Electronic Resource
    Classification of invariant wave equations (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 6414-6438 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper we characterize the possible symmetry groups of wave equations and certain evolutionary generalizations, in a single time variable and one or more spatial variables. Furthermore, we describe a complete classification of two-dimensional wave equations utt=F[u] and potential evolutionary equations uxt=F[u] having a point or contact symmetry group. The results rely on Lie's classification of planar transformation groups and their relative differential invariants. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531785
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  • 5
    Electronic Resource
    Electronic Resource
    Dirac's theory of constraints in field theory and the canonical form of Hamiltonian differential operators (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 2495-2501 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A simple algorithm for constructing the canonical form of Hamiltonian systems of evolution equations with constant coefficient Hamiltonian differential operators is given. The result of the construction is equivalent to the canonical system derived using Dirac's theory of constraints from the corresponding degenerate Lagrangian.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527315
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  • 6
    Electronic Resource
    Electronic Resource
    Equivalence of higher-order Lagrangians. II. The Cartan form for particle Lagrangians (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 902-906 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown how Cartan's method of equivalence may be used to obtain the Cartan form for an r th-order particle Lagrangian on the line by solving the standard equivalence problem under contact transformations on the jet bundle J r+k for k≥r−1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528358
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  • 7
    Electronic Resource
    Electronic Resource
    Hamiltonian structures for systems of hyperbolic conservation laws (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1610-1619 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The bi-Hamiltonian structure for a large class of one-dimensional hyberbolic systems of conservation laws in two field variables, including the equations of gas dynamics, shallow water waves, one-dimensional elastic media, and the Born–Infeld equation from nonlinear electrodynamics, is exhibited. For polytropic gas dynamics, these results lead to a quadri-Hamiltonian structure. New higher-order entropy-flux pairs (conservation laws) and higher-order symmetries are exhibited.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527909
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  • 8
    Electronic Resource
    Electronic Resource
    Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators (1993)
    Springer
    Communications in mathematical physics 153 (1993), S. 117-146 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We completely determine necessary and sufficient conditions for the normalizability of the wave functions giving the algebraic part of the spectrum of a quasi-exactly solvable Schrödinger operator on the line. Methods from classical invariant theory are employed to provide a complete list of canonical forms for normalizable quasi-exactly solvable Hamiltonians and explicit normalizability conditions in general coordinate systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02099042
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  • 9
    Electronic Resource
    Electronic Resource
    New quasi-exactly solvable Hamiltonians in two dimensions (1994)
    Springer
    Communications in mathematical physics 159 (1994), S. 503-537 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Quasi-exactly solvable Schrödinger operators have the remarkable property that a part of their spectrum can be computed by algebraic methods. Such operators lie in the enveloping algebra of a finite-dimensional Lie algebra of first order differential operators—the “hidden symmetry algebra”. In this paper we develop some general techniques for constructing quasi-exactly solvable operators. Our methods are applied to provide a wide variety of new explicit two-dimensional examples (on both flat and curved spaces) of quasi-exactly solvable Hamiltonians, corresponding to both semisimple and more general classes of Lie algebras.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02099982
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  • 10
    Electronic Resource
    Electronic Resource
    Integrable Evolution Equations on Associative Algebras (1998)
    Springer
    Communications in mathematical physics 193 (1998), S. 245-268 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: This paper surveys the classification of integrable evolution equations whose field variables take values in an associative algebra, which includes matrix, Clifford, and group algebra valued systems. A variety of new examples of integrable systems possessing higher order symmetries are presented. Symmetry reductions lead to an associative algebra-valued version of the Painlevé transcendent equations. The basic theory of Hamiltonian structures for associative algebra-valued systems is developed and the biHamiltonian structures for several examples are found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050328
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