References & Citations
Nonlinear Sciences > Exactly Solvable and Integrable Systems
Title: On Lax representations under the gauge equivalence relation and Miura-type transformations for lattice equations
(Submitted on 14 May 2024)
Abstract: We study matrix Lax representations (MLRs) for differential-difference (lattice) equations. For a given equation, two MLRs are said to be gauge equivalent if one of them can be obtained from the other by means of a matrix gauge transformation.
We present results on the following questions:
1. When is a given MLR gauge equivalent to an MLR suitable for constructing differential-difference Miura-type transformations by the method of [G. Berkeley, S. Igonin, J. Phys. A (2016), arXiv:1512.09123]?
2. When is a given MLR gauge equivalent to a trivial MLR?
Furthermore, we present new examples of integrable differential-difference equations with Miura-type transformations.
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