Li Yan-guang. Bäcklund Transformations for the Equation ∂2u/∂x1∂x1+∂2u/∂x2∂x2=f(u)[J]. Applied Mathematics and Mechanics, 1989, 10(2): 131-135.
Citation: Li Yan-guang. Bäcklund Transformations for the Equation ∂2u/∂x1∂x1+∂2u/∂x2∂x2=f(u)[J]. Applied Mathematics and Mechanics, 1989, 10(2): 131-135.

Bäcklund Transformations for the Equation ∂2u/∂x1∂x1+∂2u/∂x2∂x2=f(u)

  • Received Date: 1987-12-07
  • Publish Date: 1989-02-15
  • Bäcklund transformations for the equation ∂2u/∂x1∂x1+∂2u/∂x2∂x2=f(u) is an arbitrary function) is studied in this paper, using the procedure of Wahlquist and Estabrook (WEP). We conclude that the condition d2f/du2=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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    Leibbrandt,G.,Exact solutions of the elliptic sine equation in two space dimensions with applications to the Josephson effect,Phys.Rev.,B 15(1977),3353-3361.
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    Leibbrandt,G.,Soliton-like solutions of the elliptic sinecosine equation by means of harmonic functions,J.Math Phys.,19(1978),960-966.
    [3]
    Rogers,C.and W.F.Shadwick,Backlund Transformations and Their Applications,Academic Press(1982).
    [4]
    Segur,H.,Some open problems,Physica,18D(1986),1-12.
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