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In this work, we consider the Lie point symmetry analysis of a strongly nonlinear partial differential equation of third order, the ∞‐Polylaplacian, in two spatial dimensions. This equation is a higher order generalization of the ∞‐Laplacian, also known as Aronsson's equation, and arises as the analog of the Euler–Lagrange equations of a second‐order variational principle in L∞. We obtain its full symmetry group, one‐dimensional Lie subalgebras and the corresponding symmetry reductions to ordinary differential equations. Finally, we use the Lie symmetries to construct new invariant ∞‐Polyharmonic functions. 相似文献
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Alexander V. Mikhailov Georgios Papamikos Jing Ping Wang 《Letters in Mathematical Physics》2016,106(7):973-996
We propose a method for construction of Darboux transformations, which is a new development of the dressing method for Lax operators invariant under a reduction group. We apply the method to the vector sine-Gordon equation and derive its Bäcklund transformations. We show that there is a new Lax operator canonically associated with our Darboux transformation resulting an evolutionary differential-difference system on a sphere. The latter is a generalised symmetry for the chain of Bäcklund transformations. Using the re-factorisation approach and the Bianchi permutability of the Darboux transformations, we derive new vector Yang–Baxter map and integrable discrete vector sine-Gordon equation on a sphere. 相似文献
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Adamopoulou P. Konstantinou-Rizos S. Papamikos G. 《Theoretical and Mathematical Physics》2021,207(2):553-559
Theoretical and Mathematical Physics - We study certain extensions of the Adler map on Grassmann algebras $$\Gamma(n)$$ of order $$n$$ . We consider a known Grassmann-extended Adler map and under... 相似文献
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