||Conserved quantities of the integrable discrete hungry systems
Kakizaki, Sonomi ,
Fukuda, Akiko ,
Yamamoto, Yusaku ,
Iwasaki, Masashi ,
Ishiwata, EmikoNakamura, Yoshimasa
Discrete and Continuous Dynamical Systems - Series S
899 , 2015-10 , American Institute of Mathematical Sciences
Published: July 2015.
In this paper, conserved quantities of the discrete hungry Lotka-Volterra (dhLV) system are derived. Our approach is based on the Lax representation of the dhLV system, which expresses the time evolution of the dhLV system as a similarity transformation on a certain square matrix. Thus, coefficients of the characteristic polynomial of this matrix constitute conserved quantities of the dhLV system. These coefficients are calculated explicitly through a recurrence relation among the characteristic polynomials of its leading principal submatrices. The conserved quantities of the discrete hungry Toda (dhToda) equation is also derived with the help of the Bäcklund transformation between the dhLV system and the dhToda equation.