On a structure of the explicit solutions to the Davey - Stewartson equations
Physica D 87, 115-122 (1995)
A general representation of explicit solutions to the
Davey-Stewartson (DS) equations is obtained within the
framework of the dressing method. The structure of the
solutions with nonzero boundary values at infinity is
established to coincide with the functional structure
of the solutions to equations of the generalized KP hierarchy.
The exponential and rational-type solutions are found
both for the DS equations and for their one-dimensional
reduction, the nonlinear Schrodinger equation.
KADOMTSEV-PETVIASHVILI EQUATION, POSITIVE DISPERSION, PERIODIC SOLITON