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of 48
pro vyhledávání: '"Hay, Mike"'
We consider a Lax pair found by Xia, Qiao and Zhou for a family of two-component analogues of the Camassa-Holm equation, including an arbitrary function $H$, and show that this apparent freedom can be removed via a combination of a reciprocal transfo
Externí odkaz:
http://arxiv.org/abs/1805.03323
Autor:
Hay, Mike
Doctor of Philosophy (PhD).
The term `Lax pair' refers to linear systems (of various types) that are related to nonlinear equations through a compatibility condition. If a nonlinear equation possesses a Lax pair, then the Lax pair may be used to
The term `Lax pair' refers to linear systems (of various types) that are related to nonlinear equations through a compatibility condition. If a nonlinear equation possesses a Lax pair, then the Lax pair may be used to
Externí odkaz:
http://hdl.handle.net/2123/3958
Autor:
Butler, Samuel, Hay, Mike
Two simple ways to identify and explain fake Lax pairs are provided. The two methods are complementary, one involves finding a gauge transformation which can be used to remove the associated nonlinear system's dependent variable(s) from a fake Lax pa
Externí odkaz:
http://arxiv.org/abs/1311.2406
We present a class of reductions of M\"obius type for the lattice equations known as Q1, Q2, and Q3 from the ABS list. The deautonomised form of one particular reduction of Q3 is shown to exist on the $A_1^{(1)}$ surface which belongs to the multipli
Externí odkaz:
http://arxiv.org/abs/1307.3390
Autor:
Hay, Mike
We produce a hierarchiy of integrable equations by systematically adding terms to the Lax pair for the lattice modified KdV equation. The equations in the hierarchy are related to one aonother by recursion relations. These recursion relations are sol
Externí odkaz:
http://arxiv.org/abs/1207.4637
We present an explicit formula for the discrete power function introduced by Bobenko, which is expressed in terms of the hypergeometric \tau functions for the sixth Painlev\'e equation. The original definition of the discrete power function imposes s
Externí odkaz:
http://arxiv.org/abs/1105.1612
Autor:
Hay, Mike C.
Publikováno v:
SIGMA 7 (2011), 089, 12 pages
We expand the completeness study instigated in [J. Math. Phys. 50 (2009), 103516, 29 pages] which found all $2\times2$ Lax pairs with non-zero, separable terms in each entry of each Lax matrix, along with the most general nonlinear systems that can b
Externí odkaz:
http://arxiv.org/abs/1104.0084
Various solutions to the discrete Schwarzian KdV equation are discussed. We first derive the bilinear difference equations of Hirota type of the discrete Schwarzian KP equation, which is decomposed into three discrete two-dimensional Toda lattice equ
Externí odkaz:
http://arxiv.org/abs/1102.1829
Autor:
Hay, Mike
We propose a method by which to examine all possible partial difference Lax pairs that consist of 'two by two' discrete linear problems, where the matrices contain one separable term in each entry. We thereby derive new, higher-order versions of the
Externí odkaz:
http://arxiv.org/abs/0806.3940
Autor:
Hay, Mike1 (AUTHOR) hay.michael.c@gmail.com, Hone, Andrew N. W.2 (AUTHOR) anwh@kent.ac.uk, Novikov, Vladimir S.3 (AUTHOR) V.Novikov@lboro.ac.uk, Wang, Jing Ping4 (AUTHOR) J.Wang@kent.ac.uk
Publikováno v:
Journal of Geometric Mechanics. Dec2019, Vol. 11 Issue 4, p561-573. 13p.
