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1
Content available remote

The constants of the Volterra derivation

100%
Hegedűs P.
Open Mathematics
|
2012
|
tom 10
|
nr 3
969-973
EN
The ring of constants of the Volterra derivation is found. Confirming a conjecture of Zielinski, it is always a polynomial ring.
2
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The five-variable Volterra system

84%
Zieliński J.
Open Mathematics
|
2011
|
tom 9
|
nr 4
888-896
EN
We give a description of all polynomial constants of the five-variable Volterra derivation, hence of all polynomial first integrals of its corresponding Volterra system of differential equations. The Volterra system plays a significant role in plasma physics and population biology.
3
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Rings of constants of four-variable Lotka-Volterra systems

84%
Zieliński J.
Open Mathematics
|
2013
|
tom 11
|
nr 11
1923-1931
EN
Lotka-Volterra systems appear in population biology, plasma physics, laser physics and derivation theory, among many others. We determine the rings of constants of four-variable Lotka-Volterra derivations with four parameters C 1, C 2, C 3, C 4 ∈ k, where k is a field of characteristic zero. Thus, we give a full description of polynomial first integrals of the respective systems of differential equations.
4
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Efficient simulation of unidirectional pulse propagation in high-contrast nonlinear nanowaveguides

68%
Andreasen J., Kolesik M.
Nanoscale Systems: Mathematical Modeling, Theory and Applications
|
2013
|
tom 2
157-165
EN
This work demonstrates an improved method to simulate long-distance femtosecond pulse propagation in highcontrast nanowaveguides. Different from typical beam propagation methods, the foundational tool here is capable of simulating strong spatiotemporal waveform reshaping and extreme spectral dynamics. Meanwhile, the ability to fully capture effects due to index contrast in the transverse direction is retained, without requiring a decomposition of the electric field in terms of waveguide modes. These simulations can be computationally expensive, however, so cost is reduced in the improved method by considering only the waveguide core. Fields in the cladding are then properly accounted for through a boundary condition suitable for the case of total internal reflection.
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