Modified series of integrable discrete equations on a quadratic lattice with a nonstandard symmetry structure

We recently constructed a series of integrable discrete autonomous equations on a quadratic lattice with a nonstandard structure of higher symmetries. Here, we construct a modified series using discrete nonpoint transformations. We use both noninvertible linearizable transformations and nonpoint transformations that are invertible on the solutions of the discrete equation. As a result, we obtain several new examples of discrete equations together with their higher symmetries and master symmetries. The constructed higher symmetries give new integrable examples of five- and seven-point differential–difference equations together with their master symmetries. The method for constructing noninvertible linearizable transformations using conservation laws is considered for the first time in the case of discrete equations.