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of 240
pro vyhledávání: '"Willox, R."'
In this letter we show that the results of degree growth (algebraic entropy) calculations for lattice equations strongly depend on the initial value problem that one chooses. We consider two problematic types of initial value configurations, one with
Externí odkaz:
http://arxiv.org/abs/1909.03232
We solve the direct scattering problem for the ultradiscrete Korteweg de Vries (udKdV) equation, over $\mathbb R$ for any potential with compact (finite) support, by explicitly constructing bound state and non-bound state eigenfunctions. We then show
Externí odkaz:
http://arxiv.org/abs/1903.07315
We derive integrable equations starting from autonomous mappings with a general form inspired by the additive systems associated to the affine Weyl group E$_8^{(1)}$. By deautonomisation we obtain two hitherto unknown systems, one of which turns out
Externí odkaz:
http://arxiv.org/abs/1701.05657
Autor:
Veselov, A. P., Willox, R.
The Burchnall-Chaundy polynomials $P_n(z)$ are determined by the differential recurrence relation $$P_{n+1}'(z)P_{n-1}(z)-P_{n+1}(z)P_{n-1}'(z)=P_n(z)^2$$ with $P_{-1}=P_0(z)=1.$ The fact that this recurrence relation has all solutions polynomial is
Externí odkaz:
http://arxiv.org/abs/1407.7394
A deautonomized version of the two-dimensional Toda lattice equation is presented. Its ultra-discrete analogue and soliton solutions are also discussed.
Comment: 11 pages, LaTeX file
Comment: 11 pages, LaTeX file
Externí odkaz:
http://arxiv.org/abs/solv-int/9708001
Autor:
Nimmo, J. J. C., Willox, R.
Publikováno v:
Proceedings: Mathematical, Physical and Engineering Sciences, 1997 Dec 01. 453(1967), 2497-2525.
Externí odkaz:
https://www.jstor.org/stable/53076
Publikováno v:
Proceedings: Mathematical, Physical and Engineering Sciences, 1996 Feb 01. 452(1945), 223-234.
Externí odkaz:
https://www.jstor.org/stable/52875
Publikováno v:
Proceedings: Mathematical, Physical and Engineering Sciences, 2015 Nov 01. 471(2183), 1-20.
Externí odkaz:
https://www.jstor.org/stable/26159941
Publikováno v:
In Physica D: Nonlinear Phenomena 2009 238(22):2238-2245
Akademický článek
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