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nlin.SI2016★ 9 cited
Darboux transformations with tetrahedral reduction group and related integrable systems
George Berkeley, Alexander V. Mikhailov, Pavlos Xenitidis
In this paper we derive new two-component integrable differential difference and partial difference systems by applying a Lax-Darboux scheme to an operator formed from an ${\mathfr…
nlin.SI2015★ 8 cited
Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations
George Berkeley, Sergei Igonin
Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to constru…