Connections via B ̈acklund transformations among different non- linear evolution equations are investigated aiming to compare corresponding Abelian and non Abelian results. Specifically, links, via B ̈acklund transfor- mations, connecting Burgers and KdV-type hierarchies of nonlinear evolution equations are studied. Crucial differences as well as notable similarities be- tween Ba ̈cklund charts in the case of the Burgers - heat equation, on one side and KdV -type equations are considered. The B ̈acklund charts constructed in [16] and [17], respectively, to connect Burgers and KdV-type hierarchies of operator nonlinear evolution equations show that the structures, in the non- commutative cases, are richer than the corresponding commutative ones.
Abelian versus non-abelian baecklund charts:some remarks / Carillo, Sandra; LO SCHIAVO, Mauro; Schiebold, Cornelia. - In: EVOLUTION EQUATIONS AND CONTROL THEORY. - ISSN 2163-2480. - STAMPA. - 8:1(2019), pp. 43-55. [10.3934/eect.2019003]
Abelian versus non-abelian baecklund charts:some remarks
CARILLO, Sandra
Primo
;LO SCHIAVO, MauroSecondo
;
2019
Abstract
Connections via B ̈acklund transformations among different non- linear evolution equations are investigated aiming to compare corresponding Abelian and non Abelian results. Specifically, links, via B ̈acklund transfor- mations, connecting Burgers and KdV-type hierarchies of nonlinear evolution equations are studied. Crucial differences as well as notable similarities be- tween Ba ̈cklund charts in the case of the Burgers - heat equation, on one side and KdV -type equations are considered. The B ̈acklund charts constructed in [16] and [17], respectively, to connect Burgers and KdV-type hierarchies of operator nonlinear evolution equations show that the structures, in the non- commutative cases, are richer than the corresponding commutative ones.File | Dimensione | Formato | |
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Note: http://aimsciences.org/article/doi/10.3934/eect.2019003
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