Dark optical solitons and conservation laws to the resonance nonlinear Shrödinger's equation with Kerr law nonlinearity

In this work, we investigate the soliton solutions to the resonant nonlinear Shrödinger's equation (R-NSE) with Kerr law nonlinearity. By adopting the Riccati-Bernoulli sub-ODE technique, we present the exact dark optical, dark-singular and periodic singular soliton solutions to the model. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. We studied the R-NSE by analyzing a system of nonlinear partial differential equations (NPDEs) obtained by decomposing the equation into real and imaginary components. We derive the Lie point symmetry generators of the system, then we apply the general conservation theorem to establish a set of nontrivial and nonlocal conservation laws (Cls). Some interesting figures for the acquired solutions are Cls also presented.