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An efficient algorithm of logarithmic transformation to Hirota bilinear form of KdV-type bilinear equation. (English) Zbl 1416.65385
Summary: An efficient algorithm of logarithmic transformation to Hirota bilinear form of the KdV-type bilinear equation is established. In the algorithm, some properties of Hirota operator and logarithmic transformation are successfully applied, which helps to prove that the linear terms of the nonlinear partial differential equation play a crucial role in finding the Hirota bilinear form. Experimented with various integro-differential equations, our algorithm is proven to be more efficient than the algorithm referred by Z.-J. Zhou et al. [Appl. Math. Comput. 183, No. 2, 872–877 (2006; Zbl 1110.65098)] in getting the Hirota bilinear form, especially in achieving the coefficient of the logarithmic transformation.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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