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A class of nonlinear problems on the plane, described by nonlinear inhomogeneous ∂̄-equations, is considered. It is shown that the corresponding dynamics, generated by deformations of inhomogeneous terms (sources) is described by Hamilton-Jacobi type equations associated with hierarchies of dispersionless integrable systems. These hierarchies are… (More)
The quasi-classical ∂̄-dressing method is used to derive compact generating equations for dispersionless hierarchies. Dispersionless Kadomtsev-Petviashvili (KP) and two-dimensional Toda lattice (2DTL) hierarchies are considered as illustrative examples.
A method is given for finding the shifts in position of the solitons for the case of nonzero reflection coefficient. Expressions for boost generators in terms of scattering data play a prominent role in the analysis. Phase-shift formulas which show the effect of the radiation component on the soliton motion are deduced for the nonlinear Schrodinger… (More)
We consider the Manin-Radul and Jacobian supersymmetric KP hierarchies from the point of view of the tau-function formalism. Solutions of their associated systems of Sato equations are characterized in terms of correlation functions of supersymmetric vertex operators of superghost type. The expression of the wave functions of these hierarchies in terms of… (More)
We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden structures of the theory of integrable systems. Illustrative examples and new integrable models are exhibited.
The factorization problem of the multi-component 2D Toda hierarchy is used to analyze the dispersionless limit of this hierarchy. A dispersive version of the Whitham hierarchy defined in terms of scalar Lax and Orlov–Schulman operators is introduced and the corresponding additional symmetries and string equations are discussed. Then, it is shown how KP and… (More)
The subject of integrable nonlinear lattices is an important branch of the inverse scattering transform (IST) method. ' Many infinite families of these integrable systems can be derived and classified by means of discrete versions of the Lax-pair technique, ' and some of their members are interesting models for vastly different physical situations. As in… (More)