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The Hirato bilinear method is extended to construct quasi-periodic wave solutions for the Kersten-Krasil’shchik coupled KdV-mKdV system. One- and two-periodic wave solutions are obtained by means of a multidimensional Riemann theta function. The asymptotic property of the quasi-periodic wave solutions is proved. It is shown that the quasi-periodic wave solutions reduce to the soliton solutions in an asymptotic small amplitude limit.

Bilinear approach to quasi-periodic wave solutions of the Kersten-Krasil’shchik coupled KdV-mKdV system