New exact solitary wave solutions, bifurcation analysis and first order conserved quantities of resonance nonlinear Schrödinger’s equation with Kerr law nonlinearity

Abstract

This paper anatomizes the exact solutions of the resonant non-linear Schrödinger’s equation (R-NLSE) with the Kerr law non-linearity with the assistance of the new extended direct algebraic technique. The secured soliton erections are newfangled and unreservedly invigorating for investigators. The graphically comprehensive report of some specific solutions is embellished with the well-judged values of parameters to illustrate their propagation. Then a planer dynamical system is introduced and the bifurcation analysis has been executed to figure out the bifurcation structures of the non-linear and super non-linear traveling wave solutions of the heeded model. All possible phase portraits are exhibited with specific values of parameters. Furthermore, a precise class of non-trivial and first-order conserved quantities is enumerated by the intervention of the multiplier approach.