### Abstract

Oblique interaction of two solitons of the same amplitude in an extended Kadomtsev-Petviashvili (EKP) equation, which is a weakly two-dimensional generalization of an extended Korteweg-de Vries (EKdV) equation, is investigated. This interaction problem is solved numerically under the initial and boundary condition simulating the reflection problem of the obliquely incident soliton due to a rigid wall. The essential parameters are given by Q* ≡ aQ and Ω* ≡ Ω/a^{1/2}. Here, Q is the coefficient of the cubic nonlinear term in the EKP quation, a the amplitude of the incident soliton and ≡ ≡ tan θ_{i}, θ_{i} being the angle of incidence. The numerical solutions for various values of these parameters reveal the effect of the cubic nonlinear term on the behavior of the waves generated by the interaction. When Q* is small, the interaction property is very similar to that of the Kadomtsev-Petviashvili equation. Especially, for relatively small Ω*, a new wave of large amplitude and of soliton profile called "stem" is generated. On the other hand, when Q* is close to 6, no stem is generated owing to the existence of amplitude restriction for the soliton solution.

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

Article number | 084401 |

Journal | journal of the physical society of japan |

Volume | 76 |

Issue number | 8 |

DOIs | |

Publication status | Published - Aug 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*journal of the physical society of japan*,

*76*(8), [084401]. https://doi.org/10.1143/JPSJ.76.084401

**Oblique interaction of solitons in an extended Kadomtsev-Petviashvili equation.** / Tsuji, Hidekazu; Oikawa, Masayuki.

Research output: Contribution to journal › Article

*journal of the physical society of japan*, vol. 76, no. 8, 084401. https://doi.org/10.1143/JPSJ.76.084401

}

TY - JOUR

T1 - Oblique interaction of solitons in an extended Kadomtsev-Petviashvili equation

AU - Tsuji, Hidekazu

AU - Oikawa, Masayuki

PY - 2007/8/1

Y1 - 2007/8/1

N2 - Oblique interaction of two solitons of the same amplitude in an extended Kadomtsev-Petviashvili (EKP) equation, which is a weakly two-dimensional generalization of an extended Korteweg-de Vries (EKdV) equation, is investigated. This interaction problem is solved numerically under the initial and boundary condition simulating the reflection problem of the obliquely incident soliton due to a rigid wall. The essential parameters are given by Q* ≡ aQ and Ω* ≡ Ω/a1/2. Here, Q is the coefficient of the cubic nonlinear term in the EKP quation, a the amplitude of the incident soliton and ≡ ≡ tan θi, θi being the angle of incidence. The numerical solutions for various values of these parameters reveal the effect of the cubic nonlinear term on the behavior of the waves generated by the interaction. When Q* is small, the interaction property is very similar to that of the Kadomtsev-Petviashvili equation. Especially, for relatively small Ω*, a new wave of large amplitude and of soliton profile called "stem" is generated. On the other hand, when Q* is close to 6, no stem is generated owing to the existence of amplitude restriction for the soliton solution.

AB - Oblique interaction of two solitons of the same amplitude in an extended Kadomtsev-Petviashvili (EKP) equation, which is a weakly two-dimensional generalization of an extended Korteweg-de Vries (EKdV) equation, is investigated. This interaction problem is solved numerically under the initial and boundary condition simulating the reflection problem of the obliquely incident soliton due to a rigid wall. The essential parameters are given by Q* ≡ aQ and Ω* ≡ Ω/a1/2. Here, Q is the coefficient of the cubic nonlinear term in the EKP quation, a the amplitude of the incident soliton and ≡ ≡ tan θi, θi being the angle of incidence. The numerical solutions for various values of these parameters reveal the effect of the cubic nonlinear term on the behavior of the waves generated by the interaction. When Q* is small, the interaction property is very similar to that of the Kadomtsev-Petviashvili equation. Especially, for relatively small Ω*, a new wave of large amplitude and of soliton profile called "stem" is generated. On the other hand, when Q* is close to 6, no stem is generated owing to the existence of amplitude restriction for the soliton solution.

UR - http://www.scopus.com/inward/record.url?scp=34547907425&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34547907425&partnerID=8YFLogxK

U2 - 10.1143/JPSJ.76.084401

DO - 10.1143/JPSJ.76.084401

M3 - Article

AN - SCOPUS:34547907425

VL - 76

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 8

M1 - 084401

ER -