Titlebook: Homotopy Analysis Method in Nonlinear Differential Equations; Shijun Liao Book 2012 Higher Education Press,Beijng and Springer-Verlag GmbH

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A Boundary-layer Flow with an Infinite Number of Solutionsy decaying solutions of a nonlinear boundary-value equation in an infinite interval. Especially, an infinite number of algebraically decaying solutions were found for the first time by means of the HAM, which illustrate the originality and validity of the HAM for nonlinear boundary-value problems.

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Interaction of Nonlinear Water Wave and Nonuniform Currents of a periodic traveling wave on a non-uniform current with exponential distribution of vorticity. In the frame of the HAM, the original highly nonlinear PDE with variable coefficient is transferred into an infinite number of much simpler linear PDEs, which are rather easy to solve. Physically, it i

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Resonance of Arbitrary Number of Periodic Traveling Water Wavesion 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, wh