English

Explicit solutions for a (2+1)-dimensional Toda-like chain

Exactly Solvable and Integrable Systems 2013-09-04 v1 Mathematical Physics math.MP

Abstract

We consider a (2+1)-dimensional Toda-like chain which can be viewed as a two-dimensional generalization of the Wu-Geng model and which is closely related to the two-dimensional Volterra, two-dimensional Toda and relativistic Toda lattices. In the framework of the Hirota direct approach, we present equations describing this model as a system of bilinear equations that belongs to the Ablowitz-Ladik hierarchy. Using the Jacobi-like determinantal identities and the Fay identity for the theta-functions, we derive its Toeplitz, dark-soliton and quasiperiodic solutions as well as the similar set of solutions for the two-dimensional Volterra chain.

Keywords

Cite

@article{arxiv.1301.0414,
  title  = {Explicit solutions for a (2+1)-dimensional Toda-like chain},
  author = {V. E. Vekslerchik},
  journal= {arXiv preprint arXiv:1301.0414},
  year   = {2013}
}
R2 v1 2026-06-21T23:03:18.991Z