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Publisher
Springer, Berlin, Heidelberg
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Authors: Shijun Liao
Publish Date: 2012
Volume: , Issue: , Pages: 523-562
Abstract
In this chapter we verify the validity of the homotopy analysis method HAM for a rather complicated nonlinear PDE describing the nonlinear interaction of arbitrary number of traveling water waves In the frame of the HAM the waveresonance criterion for arbitrary number of waves is gained for the first time which logically contains the famous Phillips’ criterion for four small amplitude waves Besides it is found for the first time that when the waveresonance criterion is satisfied and the wave system is fully developed there exist multiple steadystate resonant waves whose amplitude might be much smaller than primary waves so that a resonant wave may contain much small percentage of the total wave energy This example illustrates that the HAM can be used as a tool to deepen and enrich our understandings about some rather complicated nonlinear phenomena
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