The first integral method to the nonlinear Schrödinger equations in higher dimensions (Q1949450)

Summary: The first integral method introduced by \textit{Z. Feng} [J. Phys. A, Math. Gen. 35, No. 2, 343--349 (2002; Zbl 1040.35096)] is adopted for solving some important nonlinear partial differential equations, including the \((2 + 1)\)-dimensional hyperbolic nonlinear Schrödinger (HNLS) equation, the generalized nonlinear Schrödinger (GNLS) equation with a source, and the higher-order nonlinear Schrödinger equation in nonlinear optical fibers. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner.