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math-ph2009★ 3 cited
A nonstationary form of the range refraction parabolic equation and its application as an artificial boundary condition for the wave equation in a waveguide
P. S. Petrov, M. Yu. Trofimov
The time-dependent form of Tappert's range refraction parabolic equation is derived using Daletskiy-Krein formula form noncommutative analysis and proposed as an artificial boundar…
math-ph2006
A new approach to the absorbing boundary conditions for the Schrödinger type equations
M. Yu. Trofimov
By the multiple-scale method some new approximate absorbing boundary conditions for the Schrödinger type equations are obtained.