Some novel nonlinear coherent excitations of the Davey–Stewartson system

Abstract

Exact solutions of many integrable (2 + 1) (2 spatial and 1 temporal) dimensional systems of nonlinear evolution equations, e.g., the Davey–Stewartson model, can be obtained by a special separation of variables procedure. By choosing the Jacobi elliptic functions as the building blocks, exact, doubly periodic solutions are obtained analytically. Here, two sets of elliptic functions with two different, independent moduli are employed, and the resulting wave packets are expressed as rational functions of elliptic functions. By taking the long wave limit in one spatial variable, peculiar wave patterns localized in one direction, but periodic in the other direction, will arise. By taking the long wave limit in both spatial variables, exponentially localized wave patterns which differ from the known dromions will result. The boundary conditions relating to these localized structures are studied.