DC power-bus modeling and design with a mixed-potential integral-equation formulation and circuit extraction

2001 ◽  
Vol 43 (4) ◽  
pp. 426-436 ◽  
Author(s):  
Jun Fan ◽  
J.L. Drewniak ◽  
Hao Shi ◽  
J.L. Knighten
Keyword(s):  
Integral Equation ◽  
Mixed Potential ◽  
Equation Formulation ◽  
Power Bus ◽  
Dc Power ◽  
Circuit Extraction ◽  
Integral Equation Formulation

On periodic water-waves and their convergence to solitary waves in the long-wave limit

1981 ◽  
Vol 303 (1481) ◽  
pp. 633-669 ◽  
Keyword(s):  
Integral Equation ◽  
Solitary Waves ◽  
Water Waves ◽  
Periodic Problem ◽  
Existence Theory ◽  
Periodic Waves ◽  
Equation Formulation ◽  
Long Wave ◽  
Integral Equation Formulation ◽  
Wave Limit

A detailed discussion of Nekrasov’s approach to the steady water-wave problems leads to a new integral equation formulation of the periodic problem. This development allows the adaptation of the methods of Amick & Toland (1981) to show the convergence of periodic waves to solitary waves in the long-wave limit. In addition, it is shown how the classical integral equation formulation due to Nekrasov leads, via the Maximum Principle, to new results about qualitative features of periodic waves for which there has long been a global existence theory (Krasovskii 1961, Keady & Norbury 1978).

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