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

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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.

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)

Abstract

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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