Abstract
We present a paper on the different methods for finding solutions to the Caudrey–Dodd–Gibbon equation with variable coefficients, which has wide applications in quantum mechanics and nonlinear optics. We have studied the equation analytically by using the unified method and the modified Kudryashov method. With the aid of symbolic computation and several types of auxiliary equations, we have obtained soliton solutions and other solutions. Then, we assign different values to the parameters, generating two-dimensional and three-dimensional graphics of the solutions, and discuss the interaction of several groups of solion solutions to form periodic wave solutions and kink solitary wave solutions.
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