Relationships between symmetries depending on arbitrary functions and integrals of discrete equations

@article{Startsev2016RelationshipsBS,
  title={Relationships between symmetries depending on arbitrary functions and integrals of discrete equations},
  author={S Ya Startsev},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2016},
  volume={50}
}
  • S. Startsev
  • Published 7 November 2016
  • Mathematics
  • Journal of Physics A: Mathematical and Theoretical
The paper is devoted to the conjecture that an equation is Darboux integrable if and only if it possesses symmetries that depend on arbitrary functions. We note that the results of previous works together prove this conjecture for scalar partial differential equations of the form uxy=F(x,y,u,ux,uy). For autonomous semi-discrete and discrete analogues of these equations, we prove that the sequence of Laplace invariants is terminated by zero for an equation if this equation admits an operator… 

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