Conserved quantities of the integrable discrete hungry systems

Sonomi Kakizaki; Akiko Fukuda; Yusaku Yamamoto; Masashi Iwasaki; Emiko Ishiwata; Yoshimasa Nakamura

doi:10.3934/dcdss.2015.8.889

Conserved quantities of the integrable discrete hungry systems

Sonomi Kakizaki, Akiko Fukuda, Yusaku Yamamoto, Masashi Iwasaki, Emiko Ishiwata, Yoshimasa Nakamura

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	889-899
Number of pages	11
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	8
Issue number	5
DOIs	https://doi.org/10.3934/dcdss.2015.8.889
Publication status	Published - 2015 Oct 1

Keywords

Characteristic polynomial
Conserved quantities
Discrete hungry Lotka-Volterra system
Discrete hungry Toda equation
Leading principal submatrix

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcdss.2015.8.889

Cite this

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abstract = "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 B{\"a}cklund transformation between the dhLV system and the dhToda equation.",

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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

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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.

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Conserved quantities of the integrable discrete hungry systems

Abstract

Keywords

ASJC Scopus subject areas

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