Integrable discretizations for the short-wave model of the Camassa-Holm equation

Bao Feng Feng; Ken Ichi Maruno; Yasuhiro Ohta

doi:10.1088/1751-8113/43/26/265202

Integrable discretizations for the short-wave model of the Camassa-Holm equation

Bao Feng Feng^*, Ken Ichi Maruno, Yasuhiro Ohta

^*Corresponding author for this work

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

24 Citations (Scopus)

Abstract

The link between the short-wave model of the Camassa-Holm equation (SCHE) and bilinear equations of the two-dimensional Toda lattice equation is clarified. The parametric form of the N-cuspon solution of the SCHE in Casorati determinant is then given. Based on the above finding, integrable semi-discrete and full-discrete analogues of the SCHE are constructed. The determinant solutions of both semi-discrete and fully discrete analogues of the SCHE are also presented.

Original language	English
Article number	265202
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	43
Issue number	26
DOIs	https://doi.org/10.1088/1751-8113/43/26/265202
Publication status	Published - 2010
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Modelling and Simulation
Mathematical Physics
Physics and Astronomy(all)

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title = "Integrable discretizations for the short-wave model of the Camassa-Holm equation",

abstract = "The link between the short-wave model of the Camassa-Holm equation (SCHE) and bilinear equations of the two-dimensional Toda lattice equation is clarified. The parametric form of the N-cuspon solution of the SCHE in Casorati determinant is then given. Based on the above finding, integrable semi-discrete and full-discrete analogues of the SCHE are constructed. The determinant solutions of both semi-discrete and fully discrete analogues of the SCHE are also presented.",

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AU - Feng, Bao Feng

AU - Maruno, Ken Ichi

AU - Ohta, Yasuhiro

PY - 2010

Y1 - 2010

N2 - The link between the short-wave model of the Camassa-Holm equation (SCHE) and bilinear equations of the two-dimensional Toda lattice equation is clarified. The parametric form of the N-cuspon solution of the SCHE in Casorati determinant is then given. Based on the above finding, integrable semi-discrete and full-discrete analogues of the SCHE are constructed. The determinant solutions of both semi-discrete and fully discrete analogues of the SCHE are also presented.

AB - The link between the short-wave model of the Camassa-Holm equation (SCHE) and bilinear equations of the two-dimensional Toda lattice equation is clarified. The parametric form of the N-cuspon solution of the SCHE in Casorati determinant is then given. Based on the above finding, integrable semi-discrete and full-discrete analogues of the SCHE are constructed. The determinant solutions of both semi-discrete and fully discrete analogues of the SCHE are also presented.

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JF - Journal of Physics A: Mathematical and Theoretical

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ER -

Integrable discretizations for the short-wave model of the Camassa-Holm equation

Abstract

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