Abstract
This paper studies exact solutions for the (2+1)-dimensional nonlinear Schrödinger equation with variable coefficients. First, after a transformation, the linear equation is attribute to the Hukuhara equation and then it is solved by the similarity construction method. Then, the bright and dark soliton and exact solutions for the above nonlinear equation are obtained. Finally, the graphs of these exact solutions to the linear and nonlinear equations with k=1,2 are drew, respectively, which reveals that the essential profile of solutions to the nonlinear Schrödinger equation with variable coefficients is determined by the corresponding linear equation.
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