A hierarchy of differential-difference equations,conservation laws and new integrable coupling system |
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| Institution: | 1. School of Remote Sensing, Nanjing University of Information Science and Technology, Nanjing 210044, China;2. School of Statistics and Mathematics, Shandong Economic University, Jinan 250014, China;1. College of Arts and Sciences, Shanghai Maritime University, Shanghai 201306, PR China;2. School of Mathematical Sciences, Institute of Mathematics and Key Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai 200433, PR China;3. Department of Mathematics, Shanghai Second Polytechnic University, Shanghai 201209, PR China;1. Department of Physics, Swansea University, Swansea, SA2 8PP, UK;2. Departamento de Física de Partículas and IGFAE, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain |
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| Abstract: | Starting from a discrete spectral problem with two arbitrary parameters, a hierarchy of nonlinear differential-difference equations is derived. The new hierarchy not only includes the original hierarchy, but also the well-known Toda equation and relativistic Toda equation. Moreover, infinitely many conservation laws for a representative discrete equation are given. Further, a new integrable coupling system of the resulting hierarchy is constructed. |
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