TY - JOUR
T1 - Conserved quantities of the integrable discrete hungry systems
AU - Kakizaki, Sonomi
AU - Fukuda, Akiko
AU - Yamamoto, Yusaku
AU - Iwasaki, Masashi
AU - Ishiwata, Emiko
AU - Nakamura, Yoshimasa
PY - 2015/10/1
Y1 - 2015/10/1
N2 - 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.
AB - 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.
KW - Characteristic polynomial
KW - Conserved quantities
KW - Discrete hungry Lotka-Volterra system
KW - Discrete hungry Toda equation
KW - Leading principal submatrix
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U2 - 10.3934/dcdss.2015.8.889
DO - 10.3934/dcdss.2015.8.889
M3 - Article
AN - SCOPUS:84936761869
SN - 1937-1632
VL - 8
SP - 889
EP - 899
JO - Discrete and Continuous Dynamical Systems - Series S
JF - Discrete and Continuous Dynamical Systems - Series S
IS - 5
ER -