### Abstract

An integrable semi-discretization of the Camassa-Holm (CH) equation is presented. The keys of its construction are bilinear forms and determinant structure of solutions of the CH equation. Determinant formulas of N-soliton solutions of the continuous and semi-discrete Camassa-Holm equations are presented. Based on determinant formulas, we can generate multi-soliton, multi-cuspon and multi-soliton-cuspon solutions. Numerical computations using the integrable semi-discrete Camassa-Holm equation are performed. It is shown that the integrable semi-discrete Camassa-Holm equation gives very accurate numerical results even in the cases of cuspon-cuspon and soliton-cuspon interactions. The numerical computation for an initial value condition, which is not an exact solution, is also presented.

Original language | English |
---|---|

Article number | 355205 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 41 |

Issue number | 35 |

DOIs | |

Publication status | Published - 2008 Sep 5 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*41*(35), [355205]. https://doi.org/10.1088/1751-8113/41/35/355205

**An integrable semi-discretization of the Camassa-Holm equation and its determinant solution.** / Ohta, Yasuhiro; Maruno, Kenichi; Feng, Bao Feng.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 41, no. 35, 355205. https://doi.org/10.1088/1751-8113/41/35/355205

}

TY - JOUR

T1 - An integrable semi-discretization of the Camassa-Holm equation and its determinant solution

AU - Ohta, Yasuhiro

AU - Maruno, Kenichi

AU - Feng, Bao Feng

PY - 2008/9/5

Y1 - 2008/9/5

N2 - An integrable semi-discretization of the Camassa-Holm (CH) equation is presented. The keys of its construction are bilinear forms and determinant structure of solutions of the CH equation. Determinant formulas of N-soliton solutions of the continuous and semi-discrete Camassa-Holm equations are presented. Based on determinant formulas, we can generate multi-soliton, multi-cuspon and multi-soliton-cuspon solutions. Numerical computations using the integrable semi-discrete Camassa-Holm equation are performed. It is shown that the integrable semi-discrete Camassa-Holm equation gives very accurate numerical results even in the cases of cuspon-cuspon and soliton-cuspon interactions. The numerical computation for an initial value condition, which is not an exact solution, is also presented.

AB - An integrable semi-discretization of the Camassa-Holm (CH) equation is presented. The keys of its construction are bilinear forms and determinant structure of solutions of the CH equation. Determinant formulas of N-soliton solutions of the continuous and semi-discrete Camassa-Holm equations are presented. Based on determinant formulas, we can generate multi-soliton, multi-cuspon and multi-soliton-cuspon solutions. Numerical computations using the integrable semi-discrete Camassa-Holm equation are performed. It is shown that the integrable semi-discrete Camassa-Holm equation gives very accurate numerical results even in the cases of cuspon-cuspon and soliton-cuspon interactions. The numerical computation for an initial value condition, which is not an exact solution, is also presented.

UR - http://www.scopus.com/inward/record.url?scp=49749095564&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49749095564&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/41/35/355205

DO - 10.1088/1751-8113/41/35/355205

M3 - Article

AN - SCOPUS:49749095564

VL - 41

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 35

M1 - 355205

ER -