Abstract
Based on the new mapping approach and the new extended auxiliary equation approach, we obtain solitons and other solutions of the (2+1)-dimensional coupled nonlinear Schrödinger equations (NLSE). Bright, dark and singular soliton solutions as well as Jacobi elliptic function solutions, solitary wave solutions and trigonometric function solutions are found. This equation describes the transverse effects in an optical fiber, time-independent corporation and field of optical soliton.