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Transformation for the Solutions of the Two-Dimensional Toda Lattice

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Nonlinear Physics

Part of the book series: Research Reports in Physics ((RESREPORTS))

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Abstract

In the development of soliton theory, various exact methods were found for solving nonlinear evolution equations. Among them, the bilinear transformation method [1] initiated by Hirota is a powerful tool. In the bilinear formalism, a given nonlinear equation is first transformed into a bilinear form through a dependent variable transformation. Then the N-soliton solutions, the Bäcklund transformations and an infinite number of conservation laws of this bilinear equation can be derived in a systematic way.

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References

  1. Y. Matl Aino Bilinear Transformation Method, Academic Press, New York, 1964.

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  2. A. Nakamura, Exact cylindrical solitons of the sine-Gordon equation, the sinh-Gordon equation and the periodic Toda equation, J.Phys. Soc.Japan 57 (1988), 3309–3322.

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  3. A. Nakamura, A bilinear N-soliton formula for the KP equation, J. Phys.Soc.Japan 58 (1989), 412–422.

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  4. A. Nakamura, Exact Bessel type solution of the two-dimensional Toda lattice equation, J.Phys.Soc.Japan 52 (1983), 380–387.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Shanghai University of Science and Technology, Shanghai, People’s Rep. of China

    Qiming Liu

Authors
  1. Qiming Liu
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Editor information

Editors and Affiliations

  1. University of Science and Technology of China, 230026, Hefei, Anhui, People’s Rep. of China

    Chaohao Gu  & Yishen Li  & 

  2. Computing Center of Academia Sinica, 100080, Beijing, People’s Rep. of China

    Guizhang Tu

  3. Department of Mathematics, University of Science and Technology of China, 230026, Hefei, Anhui, People’s Rep. of China

    Yunbo Zeng

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© 1990 Springer-Verlag Berlin, Heidelberg

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Liu, Q. (1990). Transformation for the Solutions of the Two-Dimensional Toda Lattice. In: Gu, C., Li, Y., Tu, G., Zeng, Y. (eds) Nonlinear Physics. Research Reports in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84148-4_23

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  • DOI: https://doi.org/10.1007/978-3-642-84148-4_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52389-5

  • Online ISBN: 978-3-642-84148-4

  • eBook Packages: Springer Book Archive

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