Affiliation:
1. Institute of Applied Mathematics Department of Mathematics Faculty of Science, Beijing University of Technology Beijing P. R. China
2. School of Mathematical Sciences Capital Normal University Beijing P. R. China
Abstract
AbstractIn this paper, we first extend the hungry Lotka–Volterra lattice to a case of nonzero boundary conditions and present its corresponding exact solution expressed in terms of a block‐Hankel determinant. Then, we establish a connection between this hungry Lotka–Volterra lattice under nonzero boundary conditions and a set of biorthogonal polynomials. It turns out that the hungry Lotka–Volterra lattice under nonzero boundary conditions possesses a Lax pair expressed in terms of the biorthogonal polynomials. Moreover, we consider two special cases of the hungry Lotka–Volterra lattice. For the case , it reduces to the Lotka–Volterra lattice under nonzero boundary condition, which has been discussed in literature. We also present the result for in detail, which extends a known result to a case of nonzero boundary functions. All these results are obtained by virtue of Hirota's bilinear method and determinant techniques.
Funder
Beijing Municipal Natural Science Foundation
National Natural Science Foundation of China
Reference84 articles.
1. Linear algebra algorithms as dynamical systems
2. Discrete-time Volterra chain and classical orthogonal polynomials
3. Elliptic hypergeometric Laurent biorthogonal polynomials with a dense point spectrum on the unit circle;Tsujimoto S;Symmetry Integr Geom,2009