Darboux transformation for classical acoustic spectral problem.
Darboux transformation for the nonstationary Schrödinger equation.
Diophantine conditions in global well-posedness for coupled KdV-type systems.
Discrete isothermic surfaces.
Dispersionless Hirota equations of two-component BKP hierarchy.
Divergences in formal variational calculus and boundary terms in Hamiltonian formalism
It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.
Do all integrable evolution equations have the Painlevé property?
Drinfeld-Sokolov hierarchies on truncated current Lie algebras
In this paper we construct on truncated current Lie algebras integrable hierarchies of partial differential equations, which generalize the Drinfeld-Sokolov hierarchies defined on Kac-Moody Lie algebras.
Dubrovin Type Equations for Completely Integrable Systems Associated with a Polynomial Pencil
Dubrovin type equations for the N -gap solution of a completely integrable system associated with a polynomial pencil is constructed and then integrated to a system of functional equations. The approach used to derive those results is a generalization of the familiar process of finding the 1-soliton (1-gap) solution by integrating the ODE obtained from the soliton equation via the substitution u = u(x + λt).