Kazunori Shinohara1
CMES-Computer Modeling in Engineering & Sciences, Vol.115, No.2, pp. 149-215, 2018, DOI: 10.3970/cmes.2018.02179
Abstract Exact solutions of the cubic Duffing equation with the initial conditions are presented. These exact solutions are expressed in terms of leaf functions and trigonometric functions. The leaf function r=sleafn(t) or r=cleafn(t) satisfies the ordinary differential equation dx2/dt2=-nr2n-1. The second-order differential of the leaf function is equal to -n times the function raised to the (2n-1) power of the leaf function. By using the leaf functions, the exact solutions of the cubic Duffing equation can be derived under several conditions. These solutions are constructed using the integral functions of leaf functions sleaf2(t) and cleaf2(t) for the phase of a trigonometric… More >
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