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Linearizing integral transform for the multicomponent lattice KP

Author

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  • Capel, H.W.
  • Wiersma, G.L.
  • Nijhoff, F.W.

Abstract

We present a generalization of the direct linearization method for the Kadomtsev-Petviashvili (KP) equation and its lattice analogues such as the two-dimensional Toda equation. The generalization consists of a Riemann-Hilbert type of integral transform which relates solutions of the associated spectral problem to any given solution of the spectral problem. By dimensional reduction we obtain the integral transform for the Korteweg-de Vries (KdV) equation and its lattice analogues. The integral transform is well suited for the investigation of the finite-matrix generalizations of the above mentioned equations. Such finite-matrix generalizations may be of use in connection with partial difference equations for spin correlation functions in the two-dimensional Ising model.

Suggested Citation

  • Capel, H.W. & Wiersma, G.L. & Nijhoff, F.W., 1986. "Linearizing integral transform for the multicomponent lattice KP," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 138(1), pages 76-99.
    • Handle: RePEc:eee:phsmap:v:138:y:1986:i:1:p:76-99
    DOI: 10.1016/0378-4371(86)90174-3
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    1. van der Linden, J. & Nijhoff, F.W. & Capel, H.W. & Quispel, G.R.W., 1986. "Linear integral equations and multicomponent nonlinear integrable systems I," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 137(1), pages 44-80.
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    1. van der Linden, J. & Capel, H.W. & Nijhoff, F.W., 1989. "Linear integral equations and multicomponent nonlinear integrable systems II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 160(2), pages 235-273.

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