Abstract
The nonlinear Schrödinger equation (NLS) is widely used in different branches of physics. The GP equation is a kind of NLS equation with potential function term. In this paper, the soliton solutions of a generalized GP equation are explored. Firstly, we construct the Lax pair and Darboux transform(DT) of the equation. Then, we solve the single and double soliton solutions of the equation. Lastly, we draw the images of the single and double soliton solutions, and investigate the properties of the solitons. It is found that the amplitude of a single solitary wave does not change, and the shape and amplitude of the double solitary wave remain unchanged after the collision.
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