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The exact vortex soliton solutions of the quasi-two-dimensional cubic–quintic Gross–Pitaevskii equation with spatially inhomogeneous nonlinearities are constructed by similarity transformation. It is demonstrated that spatially inhomogeneous cubic–quintic nonlinearity can support exact vortex solitons in which there are two quantum numbers S and m. The radius structures and density distributions of...
In this Letter, a new mapping method is proposed for constructing more exact solutions of nonlinear partial differential equations. With the aid of symbolic computation, we choose the (2+1)-dimensional Konopelchenko–Dubrovsky equation and the (2+1)-dimensional KdV equations to illustrate the validity and advantages of the method. As a result, many new and more general exact solutions are obtained.
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