The research interests of Alexandre M. Vinogradov were also motivated by problems of contemporary physics – for example the structure of Hamiltonian mechanics [23], [24], the dynamics of acoustic beams [17], the equations of magnetohydrodynamics (the so-called Kadomtsev-Pogutse equations appearing in the stability theory of high-temperature plasma in tokamaks) [18] and mathematical questions in general relativity [19], [20], [21].