New exact solitary wave solutions, bifurcation analysis and rst order
conserved quantities of resonance nonlinear Shr¨odinger’s equation with
Kerr law nonlinearity
Abstract
The paper investigates exact solutions of the resonant nonlinear
Shr¨odinger’s equation (RNLSE) with Kerr law nonlinearity by using the
extended direct algebraic method. Graphs of some obtained solutions are
presented with dierent values of parameters to describe their
propagation. In order to understand the bifurcation structure of
nonlinear and super-nonlinear travelling wave solutions of the
considered equation, bifurcation analysis has been practiced. Moreover,
a set of non-trivial and rst-order conserved quantities are computed by
multiplier approach.