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Keywords = 2D dispersionless toda lattice equation with self-consistent sources

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13 pages, 265 KB  
Article
Two-Dimensional Dispersionless Toda Lattice Hierarchy: Symmetry, New Extension, Hodograph Solutions, and Reduction
by Hongxia Wu, Jingxin Liu and Haifeng Wang
Mathematics 2024, 12(23), 3706; https://doi.org/10.3390/math12233706 - 26 Nov 2024
Viewed by 850
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Modern Methods and Applications Related to Integrable Systems)
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