LAUSR

Abstract We investigate the generalized inhomogeneous NLS equation with symmetric potentials. Corresponding Lax pair is constructed through AKNS procedure. Based on the obtained Lax pair, one and two soliton solutions are generated via Darboux transformation technique. Using the obtained soliton solution, the impact of symmetric potentials on soliton dynamics is investigated. By tailoring the dispersion and nonlinearity coefficients, propagation properties of solitons are analyzed. Especially, properties of oscillating solitons and tunneling behavior are investigated. From the results, we have found that the symmetric potentials have strong influence on soliton dynamics such as period of oscillations, interaction behavior etc. Obtained results open a new window to controlling the soliton through symmetric potentials.