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Two-Dimensional Dispersionless Toda Lattice Hierarchy: Symmetry, New Extension, Hodograph Solutions, and Reduction

Author

Listed:
  • Hongxia Wu

    (Department of Mathematics, School of Science, Jimei University, Xiamen 361021, China)

  • Jingxin Liu

    (Tianjin Computer Vocational School, Tianjin 300299, China)

  • Haifeng Wang

    (Department of Mathematics, School of Science, Jimei University, Xiamen 361021, China)

Abstract
The symmetry for two-dimensional (2D) dispersionless Toda lattice hierarchy (dTLH) is firstly derived, and then the 2D dTLH is extended based on the symmetry constraint. The commutativity of two different flows for this new hierarchy is shown, which leads to the 2D dToda lattice equation with self-consistent sources (dTLESCSs) together with its conservation equation. The hodograph solutions to 2D dTLESCSs are also given. One dimensional reduction of extended 2D dTLH is finally investigated by finding the constraint, and a one-dimensional dTLESCS is shown.

Suggested Citation

  • Hongxia Wu & Jingxin Liu & Haifeng Wang, 2024. "Two-Dimensional Dispersionless Toda Lattice Hierarchy: Symmetry, New Extension, Hodograph Solutions, and Reduction," Mathematics, MDPI, vol. 12(23), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3706-:d:1530041
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