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The homogeneous balance method, Lax pair, Hirota transformation and a general fifth-order KdV equation

Yang Lei·Zhang Fajiang·Wang Yinghai
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Abstract

In this paper, some notes of the homogeneous balance (HB) method are discussed by a kind of general fifth-order KdV (fKdV) equation. Frist, the auto-Bäcklund transformation and lax represents of the higher-order KdV equation(a specific forms of fKdV equation) are obtained by the HB method. Then, the connection of the Hirota transformation and the HB method is discussed by two specific fKdV equations: the Sawada-Kotera equation and the Lax's equation. At the same time, the solitary wave solution of the general fifth-order KdV equation is obtained.

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Yang Lei, Zhang Fajiang, Wang Yinghai. 2001-08-15. The homogeneous balance method, Lax pair, Hirota transformation and a general fifth-order KdV equation. https://doi.org/10.1016/s0960-0779(00)00274-5

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