Abstract
The exact explicit traveling solutions to the two completely integrable sixth-order nonlinear equations KdV6 are given by using the method of dynamical systems and Cosgrove’s work. It is proved that these traveling wave solutions correspond to some orbits in the 4-dimensional phase space of two 4-dimensional dynamical systems. These orbits lie in the intersection of two level sets defined by two first integrals.
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Project supported by the National Natural Science Foundation of China (Nos. 10771196, 10831003) and the Innovation Project of Zhejiang Province (No. T200905).
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Li, J., Zhang, Y. The exact traveling wave solutions to two integrable KdV6 equations. Chin. Ann. Math. Ser. B 33, 179–190 (2012). https://doi.org/10.1007/s11401-012-0704-5
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DOI: https://doi.org/10.1007/s11401-012-0704-5