Deep-water and shallow-water limits of statistical equilibria for the
intermediate long wave equation
Deep-water and shallow-water limits of statistical equilibria for the
intermediate long wave equation
We study the construction of invariant measures associated with higher order conservation laws of the intermediate long wave equation (ILW) and their convergence properties in the deep-water and shallow-water limits. By exploiting its complete integrability, we first carry out detailed analysis on the construction of appropriate conservation laws of ILW …