Two-Dimensional Dispersionless Toda Lattice Hierarchy: Symmetry, New Extension, Hodograph Solutions, and Reduction
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-c...
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2024-11-01
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| author | Hongxia Wu Jingxin Liu Haifeng Wang |
| author_facet | Hongxia Wu Jingxin Liu Haifeng Wang |
| author_sort | Hongxia Wu |
| collection | DOAJ |
| description | 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. |
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| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
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| spelling | doaj-art-035567a890c2489e836c44f68c1f6e662024-12-13T16:27:29ZengMDPI AGMathematics2227-73902024-11-011223370610.3390/math12233706Two-Dimensional Dispersionless Toda Lattice Hierarchy: Symmetry, New Extension, Hodograph Solutions, and ReductionHongxia Wu0Jingxin Liu1Haifeng Wang2Department of Mathematics, School of Science, Jimei University, Xiamen 361021, ChinaTianjin Computer Vocational School, Tianjin 300299, ChinaDepartment of Mathematics, School of Science, Jimei University, Xiamen 361021, ChinaThe 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.https://www.mdpi.com/2227-7390/12/23/3706symmetryextended 2D dispersionless toda lattice hierarchy2D dispersionless toda lattice equation with self-consistent sourceshodograph solutionsone-dimensional reduction |
| spellingShingle | Hongxia Wu Jingxin Liu Haifeng Wang Two-Dimensional Dispersionless Toda Lattice Hierarchy: Symmetry, New Extension, Hodograph Solutions, and Reduction Mathematics symmetry extended 2D dispersionless toda lattice hierarchy 2D dispersionless toda lattice equation with self-consistent sources hodograph solutions one-dimensional reduction |
| title | Two-Dimensional Dispersionless Toda Lattice Hierarchy: Symmetry, New Extension, Hodograph Solutions, and Reduction |
| title_full | Two-Dimensional Dispersionless Toda Lattice Hierarchy: Symmetry, New Extension, Hodograph Solutions, and Reduction |
| title_fullStr | Two-Dimensional Dispersionless Toda Lattice Hierarchy: Symmetry, New Extension, Hodograph Solutions, and Reduction |
| title_full_unstemmed | Two-Dimensional Dispersionless Toda Lattice Hierarchy: Symmetry, New Extension, Hodograph Solutions, and Reduction |
| title_short | Two-Dimensional Dispersionless Toda Lattice Hierarchy: Symmetry, New Extension, Hodograph Solutions, and Reduction |
| title_sort | two dimensional dispersionless toda lattice hierarchy symmetry new extension hodograph solutions and reduction |
| topic | symmetry extended 2D dispersionless toda lattice hierarchy 2D dispersionless toda lattice equation with self-consistent sources hodograph solutions one-dimensional reduction |
| url | https://www.mdpi.com/2227-7390/12/23/3706 |
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