1991
DOI: 10.1364/josab.8.000413
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High-order generalized propagation techniques

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Cited by 23 publications
(18 citation statements)
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“…Higher-order schemes, yielding more accurate solutions [e.g., with accuracy OΔz 2 , OΔz 4 , etc. ], are well-known [2,3], but here we will restrict our attention to the lowest-order scheme (2). In fact, all the results obtained below for scheme (2) also hold for the second-order accurate scheme ( [2]; [1], Section 2.4); for higher-order schemes, they can be obtained in a similar manner.…”
Section: Introductionmentioning
confidence: 75%
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“…Higher-order schemes, yielding more accurate solutions [e.g., with accuracy OΔz 2 , OΔz 4 , etc. ], are well-known [2,3], but here we will restrict our attention to the lowest-order scheme (2). In fact, all the results obtained below for scheme (2) also hold for the second-order accurate scheme ( [2]; [1], Section 2.4); for higher-order schemes, they can be obtained in a similar manner.…”
Section: Introductionmentioning
confidence: 75%
“…Earlier studies, pertaining to a single soliton [6,7], indicate that a NI of a multipulse solution will be different from a NI of the plane wave Eq. (3). Nonetheless, we will demonstrate below that some of the characteristics of the NI around a plane wave carry over to the NI around a more realistic, multipulse signal.…”
Section: Introductionmentioning
confidence: 82%
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“…Moreover, although the refractive-index profile is best resolved by the finite-element technique, the transverse spatial derivatives are most accurately evaluated with the Fourier transform procedure. The precision inherent in the Fourier representation of the transverse derivatives has in fact recently been exploited to obtain generalized multioperator procedures valid to arbitrarily high order in step-length [4], [5].…”
Section: Introductionmentioning
confidence: 99%