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Bäcklund transformations for the equation ∂2u/∂x1∂x1 + ∂2u/∂x2∂x2−f (u)

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Abstract

Bäcklund transformations for the equation ∂ 2 u/∂x1∂x 1+∂ 2u/∂x 2 ∂x 2=f (u)here f is an arbitrary function) is studied in this paper, using the procedure of Wahlquist and Estabrook (WEP). We conclude that the condition d 2 f/du 2=λf is sufficient for the existence of Bäcklund transformations for the equation of our interest. A special case of our results leads to the conclusion of Leibbrandt [1,2].

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References

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Authors and Affiliations

  1. Department of Mechanics, Peking University, Beijing

    Li Yan-guang

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  1. Li Yan-guang
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Communicated by Chien Wei-zang

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Yan-guang, L. Bäcklund transformations for the equation ∂2u/∂x1∂x1 + ∂2u/∂x2∂x2−f (u). Appl Math Mech 10, 139–143 (1989). https://doi.org/10.1007/BF02014820

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  • DOI: https://doi.org/10.1007/BF02014820

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