Positon, Negaton, Soliton and Complexiton Solutions to a Four-Dimensional Nonlinear Evolution Equation

A generalized Wronskian formulation is presented for a four-dimensional nonlinear evolution equation. The representative systems are explicitly solved by selecting a broad set of sufficient conditions which make the Wronskian determinant a solution to the bilinearized four-dimensional nonlinear evolution equation. The obtained solution formulas provide us with a comprehensive approach to construct explicit exact solutions to the four-dimensional nonlinear evolution equation, by which positons, negatons, solitons and complexitons are computed for the four-dimensional nonlinear evolution equation. Applying the Hirota's direct method, multi-soliton, non-singular complexiton, and their interaction solutions of the four-dimensional nonlinear evolution equation are also obtained.

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