Optical soliton wave solutions to the resonant Davey–Stewartson system

We investigate the resonant Davey–Stewartson (DS) system. The resonant DS system is a natural \((2+1)\)-dimensional version of the resonant nonlinear Schrödinger equation. Traveling wave solutions were found. In this paper, we demonstrate the effectiveness of the analytical methods, namely, improved \(\tan (\phi /2)\)-expansion method (ITEM) and generalized (G′/G)-expansion method for seeking more exact solutions via the resonant Davey–Stewartson system. These methods are direct, concise and simple to implement compared to other existing methods. The exact particular solutions containing four types of solutions, i.e., hyperbolic function, trigonometric function, exponential and solutions. We obtained further solutions comparing these methods with other methods. The results demonstrate that the aforementioned methods are more efficient than the multi-linear variable separation method applied by Tang et al. (Chaos Solitons Fractals 42:2707–2712, 2009). Recently the ITEM was developed for searching exact traveling wave solutions of nonlinear partial differential equations. Abundant exact traveling wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play important role in engineering and physics fields. It is shown that these methods, with the help of symbolic computation, provide a straightforward and powerful mathematical tool for solving the nonlinear problems.