Abstract :
The resonant nonlinear Schrödinger (RNLS) equation exhibits the usual cubic nonlinearity
present in the classical nonlinear Schrödinger (NLS) equation together with an additional
nonlinear term involving the modulus of the wave envelope. It arises in the context of
the propagation of long magneto-acoustic waves in cold, collisionless plasma and in capillarity
theory. Here, a natural (2 + 1) (2 spatial and 1 temporal)-dimensional version of the
RNLS equation is introduced, termed the ‘resonant’ Davey–Stewartson system. The multilinear
variable separation approach is used to generate a class of exact solutions, which will
describe propagating, doubly periodic wave patterns.
