N-Soliton Solution of the Two-Dimensional Korteweg-deVries Equation

The exact N -soliton is obtained for the two-dimentional Korteweg-deVries equation, \begin{aligned} \frac{\partial^{2}u}{\partial t\partial x}+12\frac{\partial}{\partial x}\left (u\frac{\partial u}{\partial x}\right)+\frac{\partial^{4}u}{\partial x^{4}}{\pm}12\frac{\partial^{2}u}{\partial y^{2}}{=}0, \end{aligned} through Hirota's method. The solution has the same functional from as one-dimensional case. The two-dimensional effects are also discussed.

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