Abstract: | In this talk, we mainly consider the extension of Noether's theorem to semi-discrete equations after introducing a general prolongation formula for their continuous symmetries. For differential equations, the symmetry method provides significant insights and techniques for finding exact solutions. These techniques have been generalised to discrete as well as semi-discrete equations during last decades. However, in literature, some inconsistency for symmetry analysis of semi-discrete equations was realised, which has been troublesome for quite some time. This mystery of inconsistency will be uncovered in this talk too. We will also provide an understanding of integrability via compatibility and continuoussymmetries. |