Quasi-periodic solutions for some \((2+1)\)-dimensional integrable models generated by the Jaulent-Miodek hierarchy
A couple of \(2+1\) dimensional integrable equations such as the modified Kadomtsev-Petviashvili equation are investigated, which are generated from the Jaulent-Miodek hierarchy. They are decomposed into compatible finite-dimensional integrable Hamiltonian systems, through an application of symmetry constraints to the Jaulent-Miodek spectral problem. Using the elliptic coordinates, the involutivity and the functional independence of integrals of motion are verified. Finally starting from the Able-Jacobi coordinates, quasi-periodic solutions to the resulting \(2+1\) integrable equations are derived by using the Riemann theta functions. The paper is clearly written and it is a supplement to a series of the authors' works on the topic.
scientific article; zbMATH DE number 1602281