Abstract
In this paper, the variable coefficients Davey–Stewartson system represents many physical phenomena in shallow water waves, quantum and optics, etc, is transformed directly into nonlinear ordinary differential system by using the new modification to the direct similarity reduction method. After solving the reduced system, new Jacobi, hyperbolic and periodic wave solutions are achieved for complex variable coefficients Davey–Stewartson system. The application of the new modification of the direct similarity reduction method reflects how this method is powerful, easy and simple, if it is compared with other symmetry techniques.
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