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

Li Yan-guang

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Article Navigation > 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.

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.

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

Li Yan-guang

Department of Mechanics, Peking University, Beijing

Received Date: 1987-12-07
Publish Date: 1989-02-15

Abstract

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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References(4)

References

[1]	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.
[2]	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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