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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 848-872 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown how to invert the Zakharov-Shabat eigenvalue problem for rational scattering coefficients, in order to produce potentials defined over the whole real line. The method reduces the problem to finding two semi-infinite potentials—which can be efficiently calculated using the soliton-lattice algorithm described in a previous paper. The inversion is usually unique for given rational scattering coefficients, since they usually specify the scattering data of the system uniquely. In the case of nonunique inversion, it is possible to obtain a family of potentials from the inversion. Each member of the family has the same scattering data, except for differing residues. Examples of the inversion include an ‘adiabatic' inversion pulse for use in nuclear magnetic resonance, and a demonstration of how the cubic nonlinear Schrödinger equation may be integrated.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Magnetic resonance materials in physics, biology and medicine 2 (1994), S. 279-283 
    ISSN: 1352-8661
    Keywords: selective pulse ; inverse scattering theory ; SPINCALC ; soliton pulse ; refocusing pulse ; self-focusing pulse
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Physics
    Notes: Abstract Selective pulse design for noninteracting spins is equivalent to inversion of the Bloch equations. Until recently, few analytical solutions to this problem were known. However, approaches based on inverse-scattering theory have now led to general solutions that offer ever higher precision in meeting target responses. The concept of soliton pulses (pulses that leave the spin system unaffected) turns out to be a particularly valuable one because half-solitons (both π/2 and π pulses) are inherently phase compensated. Such pulses are important for observation of shortT 2 species, where substantial signal loss could occur in any refocusing period. Multiply-selective pulses, suitable for simultaneous suppression of several “solvent” lines have been generated by inverse-scattering theory and have considerable potential in bothin vivo magnetic resonance spectroscopy and in routine high-resolution NMR. Although analytical solutions show great promise, it is likely that optimization methods will continue to be of value for the foreseeable future. The use of the SPINCALC scheme that operates in a switched stationary reference frame is illustrated through its use to design adiabatic refocusing pulses that do not lead to cumulative errors when used in multiple-echo trains.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Magnetic resonance materials in physics, biology and medicine 2 (1994), S. 379-381 
    ISSN: 1352-8661
    Keywords: selective pulses ; inverse scattering theory ; solitons
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Physics
    Notes: Abstract The soliton-lattice algorithm, an exact algebraic method of inverting the Bloch equation to obtain frequency-selective radio-frequency pulses is described. Some general properties of pulses are described that were obtained with the help of this algorithm. It is used to obtain two new pulses. A highly prefocused pulse is shown that can be used in short-echo-timein vivo 31P spectroscopic imaging, and an adiabatic selective inversion pulse is obtained.
    Type of Medium: Electronic Resource
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