The spectral problem and particular solutions to the (2+1)-dimensional integrable generalization of the Camassa–Holm equation

We represent the relation between spectral problems for (2+1)-dimensional integrable generalization of the Camassa–Holm (CH) and modified Kadomtsev–Petviashvili (mKP-2) equations through the hodograph-type transformation, which allows to establish the link between particular solutions to each of them. We represent the algorithm for construction of the particular solutions to (2+1)-dimensional generalization of CH based on the nonlocal ∂̄-problem. As examples, we present the traveling wave solutions and discuss briefly the rational solutions.