A second-order solution for the solitary wave in a rotational flow is derived. This would serve as the leading-order correction to the Korteweg–de Vries (KdV) soliton. Coefficients for the higher-order KdV equation are found from a sequence of boundary value problems. Their explicit numerical values are given for the simple example of a linear shear.
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K. W. Chow (1989) studied this question.
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