Abstract
In this paper, some new formal similarity reduction solutions for the (2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived. Firstly, we derive the similarity reduction of the NNV equation with the optimal system of the admitted one-dimensional subalgebras. Secondly, by analyzing the reduced equation, three types of similarity solutions are derived, such as multi-soliton like solutions, variable separations solutions, and KdV type solutions.
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