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Hierarchy of Combined TL-RTL Equations and an Associated (2+1)-Dimensional Lattice Equation |
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| Authors: | JIANG Qiao-Yun and ZHOU Ru-Guang |
| Institution: | 1. Department of Mathematics, Nantong University, Nantong 226007, China ;2. Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, China |
| Abstract: | A new (2+1)-dimensional lattice equation is presented based upon the first two members in the hierarchy of the combined Toda lattice and relativistic Toda lattice (TL-RTL) equations in (1+1) dimensions. A Darboux transformation for the hierarchy of the combined TL-RTL equations is constructed. Solutions of the first two members in the hierarchy of the combined TL-RTL equations, as well as the new (2+1)-dimensional lattice equation are explicitly obtained by the Darboux transformation. |
| Keywords: | combined TL-RTL equation integrable system Darboux transformation Toda lattice equation relativistic Toda lattice equation |
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