Masayuki Oikawa

Fukuoka Institute of Technology, Hukuoka, Fukuoka, Japan

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Publications (47)42.35 Total impact

  • Keisuke Nakayama · Taro Kakinuma · Hidekazu Tsuji · Masayuki Oikawa
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    ABSTRACT: Solitary waves are typical nonlinear long waves in the ocean. The two-dimensional interaction of solitary waves has been shown to be essentially different from the one-dimensional case and can be related to generation of large amplitude waves (including 'freak waves'). Concerning surface-water waves, Miles (1977) theoretically analyzed interaction of three solitary waves, which is called "resonant interaction" because of the relation among parameters of each wave. Weakly-nonlinear numerical study (Funakoshi, 1980) and fully-nonlinear one (Tanaka, 1993) both clarified the formation of large amplitude wave due to the interaction ("stem" wave) at the wall and its dependency of incident angle. For the case of internal waves, analyses using weakly nonlinear model equations (e.g. Tsuji and Oikawa, 2006) suggest also qualitatively similar results. Therefore, the aim of this study is to investigate the strongly nonlinear interaction of internal solitary waves; especially whether the resonant behavior is found or not. As a result, it is found that the amplified internal wave amplitude becomes about three times as much as the original amplitude. In contrast, a "stem" is not found to occur when the incident wave angle is more than the critical angle, which has been demonstrated in the previous studies.
    No preview · Article · Dec 2012
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    Dataset: Correction
    Gino Biondini · Ken-ichi Maruno · Masayuki Oikawa · Hidekazu Tsuji

    Full-text · Dataset · Dec 2012
  • Keisuke Nakayama · Taro Kakinuma · Hidekazu Tsuji · Masayuki Oikawa
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    ABSTRACT: To clarify the resonance of fully-nonlinear internal solitary waves which is one of the reasons for the occurrence of large amplitude internal waves, fully-nonlinear and strongly-dispersive internal wave equation model was applied, which attempted to investigate interaction of internal solitary waves in a two-dimensional plane. The 3rd order theoretical solutions for internal waves in a two-layer system was used for the initial conditions and progress of internal solitary wave was confirmed. Seven different incident wave angles were given, in which 'stem' was confirmed to appear when incident wave angle is less than critical angle. As a result, it is found that the amplified internal wave amplitude becomes about three times as much as the original amplitude.
    No preview · Article · Jan 2012
  • Hidekazu Tsuji · Masayuki Oikawa
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    ABSTRACT: Two-dimensional (2D) interactions of two interfacial solitons in a two-layer fluid of finite depth are investigated under the assumption of a small but finite amplitude. When the angle between the wave normals of two solitons is not small, it is shown by a perturbation method that in the lowest order of approximation the solution is a superposition of two intermediate long wave (ILW) solitons and in the next order of approximation the effect of the interaction appears as position phase shifts and as an increase in amplitude at the interaction center of two solitons. When is small, it is shown that the interaction is described approximately by a nonlinear integro-partial differential equation that we call the two-dimensional ILW (2DILW) equation. By solving it numerically for a V-shaped initial wave that is an appropriate initial value for the oblique reflection of a soliton due to a rigid wall, it is shown that for a relatively large angle of incidence i the reflection is regular, but for a relatively small i the reflection is not regular and a new wave called stem is generated. The results are also compared with those of the Kadomtsev–Petviashvili (KP) equation and of the two-dimensional Benjamin–Ono (2DBO) equation.
    No preview · Article · Oct 2010 · Fluid Dynamics Research
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    ABSTRACT: A set of nonlinear internal-wave equations, which have been derived on the basis of the variational principle without any assumptions concerning wave nonlinearity and dispersion, is applied to compare numerical results with experimental data of internal waves propagating in a deep-water region. Internal waves propagating over a uniformly sloping beach are also simulated. Internal progressive waves show remarkable shoaling after the interface reaches the critical level, after which the physical variables change discontinuously near the wave-breaking point. In the wave-breaking case of internal waves reflecting at a vertical wall, the vertical velocity of the particles in the vicinity of the interface is different from that of the moving interface on the wall, which means that the kinematic boundary condition on the interface is not satisfied.
    No preview · Article · Jan 2010
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    ABSTRACT: Applicability of the 3rd order theoretical solutions for internal waves in a two-layer system is investigated by using a strongly nonlinear and dispersive internal wave model. The 3rd order solution is derived using the 9th order internal wave equations. The 3rd order solution is found to give larger wavelength scale compared to KdV theory. The applicability of the 3rd order solution is confirmed to be high when the amplitude of internal solitary wave is 5% of the lower layer thickness. A fully nonlinear strongly dispersive internal wave model reveals that high frequency internal waves are induced behind an internal solitary wave when the initial shape of internal solitary wave is larger than critical level.
    No preview · Article · Jan 2010
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    Yuji Kodama · Masayuki Oikawa · Hidekazu Tsuji
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    ABSTRACT: We consider the initial value problems of the Kadomtsev-Petviashvili (KP) equation for symmetric V-shape initial waves consisting of two semi-infinite line solitons with the same amplitude. Numerical simulations show that the solutions of the initial value problem approach asymptotically to certain exact solutions of the KP equation found recently in [Chakravarty and Kodama, JPA, 41 (2008) 275209]. We then use a chord diagram to explain the asymptotic result. We also demonstrate a real experiment of shallow water wave which may represent the solution discussed in this Letter.
    Preview · Article · Aug 2009 · Journal of Physics A Mathematical and Theoretical
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    Gino Biondini · Ken-ichi Maruno · Masayuki Oikawa · Hidekazu Tsuji
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    ABSTRACT: We study the maximum wave amplitude produced by line-soliton interactions of the Kadomtsev-Petviashvili II (KPII) equation, and we discuss a mechanism of generation of large amplitude shallow water waves by multi-soliton interactions of KPII. We also describe a method to predict the possible maximum wave amplitude from asymptotic data. Finally, we report on numerical simulations of multi-soliton complexes of the KPII equation which verify the robustness of all types of soliton interactions and web-like structure. Comment: 28 pages, 11 figures. Stud. Appl. Math. vol. 122 (2009). Editorial production errors in the printed version were corrected. Several discussions about amplitude were improved. Some figures were improved
    Full-text · Article · Mar 2009 · Studies in Applied Mathematics
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    KEN-ICHI MARUNO · YASUHIRO OHTA · MASAYUKI OIKAWA
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    ABSTRACT: An integrable two-component analogue of the two-dimensional long wave-short wave resonance interaction (2c-2d-LSRI) system is studied. Wronskian solutions of 2c-2d-LSRI system are presented. A reduced case, which describes resonant interaction between an interfacial wave and two surface wave packets in a two layer fluid, is also discussed.
    Preview · Article · Feb 2009 · Glasgow Mathematical Journal
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    G. Biondini · K.-I. Maruno · M. Oikawa · H. Tsuji

    Full-text · Article · Jan 2009 · Studies in Applied Mathematics
  • Hidekazu Tsuji · Masayuki Oikawa
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    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*\equiv aQ and Omega*\equivOmega/a1/2. Here, Q is the coefficient of the cubic nonlinear term in the EKP quation, a the amplitude of the incident soliton and Omega\equiv\tanthetai, thetai 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 Omega*, 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.
    No preview · Article · Aug 2007 · Journal of the Physical Society of Japan
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    Ken-ichi Maruno · Hidekazu Tsuji · Masayuki Oikawa
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    ABSTRACT: We consider a mechanism of generation of huge waves by multi-soliton resonant interactions. A non-stationary wave amplification phenomenon is found in some exact solutions of the Kadomtsev-Petviashvili (KP) equation. The mechanism proposed here explains the character of extreme waves and of those in Tsunami.
    Preview · Article · Mar 2007
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    Yasuhiro Ohta · Ken-ichi Maruno · Masayuki Oikawa
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    ABSTRACT: The two-component analogue of two-dimensional long wave-short wave resonance interaction equations is derived in a physical setting. Wronskian solutions of the integrable two-component analogue of two-dimensional long wave-short wave resonance interaction equations are presented. Comment: 16 pages, 9 figures, revised version; The pdf file including all figures: http://www.math.utpa.edu/kmaruno/yajima.pdf
    Preview · Article · Feb 2007 · Journal of Physics A Mathematical and Theoretical
  • Masayuki Oikawa · Hidekazu Tsuji
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    ABSTRACT: Studies on the oblique interactions of weakly nonlinear long waves in dispersive systems are surveyed. We focus mainly our concentration on the two-dimensional interaction between solitary waves. Two-dimensional Benjamin–Ono (2DBO) equation, modified Kadomtsev–Petviashvili (MKP) equation and extended Kadomtsev–Petviashvili (EKP) equation as well as the Kadomtsev–Petviashvili (KP) equation are treated. It turns out that a large-amplitude wave can be generated due to the oblique interaction of two identical solitary waves in the 2DBO and the MKP equations as well as in the KP-II equation. Recent studies on exact solutions of the KP equation are also surveyed briefly.
    No preview · Article · Dec 2006 · Fluid Dynamics Research
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    A.V. Porubov · H. Tsuji · I.V. Lavrenov · M. Oikawa
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    ABSTRACT: It is shown that generation of the rogue waves in the ocean may be described in framework of non-linear two-dimensional shallow water theory where the simplest two-dimensional long wave non-linear model corresponds to the Kadomtsev–Petviashvili (KP) equation. Numerical solution of the KP equation is obtained to account for the formation of localized abnormally high amplitude wave due to a resonant superposition of two incidentally non-interacting long-crested waves. Peculiarities of the solution allow to explain rare and unexpected appearance of the rogue waves. However, our solution differs from the exact two-solitary wave solution of the KP equation used before for the rogue waves description.
    Full-text · Article · Sep 2005 · Wave Motion
  • Hidekazu Tsuji · Masayuki Oikawa
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    ABSTRACT: Two-dimensional interaction of two solitary waves is investigated numerically on the basis of a Modified Kadomtsev-Petviashvili equation. Two types of interaction are dealt with; one is the interaction of two positive solitary waves of an equal amplitude and the other is that between positive and negative solitary waves of an equal amplitude. The latter turns out to be considerably different from the former. In both cases the characteristics of the interaction depend on the ratio of a parameter representing the difference of the propagation directions of two solitary waves to the amplitude of the solitary waves. It is found that a new wave of a fairly large amplitude is produced for some range of the ratio as a result of the interaction of two positive solitary waves.
    No preview · Article · Nov 2004 · Journal of the Physical Society of Japan
  • Ken-ichi Maruno · Wen-Xiu Ma · Masayuki Oikawa
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    ABSTRACT: A set of conditions is presented for Casorati determinants to give solutions to the Toda lattice equation. It is used to establish a relation between the Casorati determinant solutions and the generalized Casorati determinant solutions. Positons, negatons and their interaction solutions of the Toda lattice equation are constructed through the generalized Casorati determinant technique. A careful analysis is also made for general positons and negatons, the resulting positons and negatons of order one being explicitly computed. The generalized Casorati determinant formulation for the two dimensional Toda lattice (2dTL) equation is presented. It is shown that positon, negaton and complexiton type solutions in the 2dTL equation exist and these solutions reduce to positon, negaton and complexiton type solutions in the Toda lattice equation by the standard reduction procedure.
    No preview · Article · Apr 2004 · Journal of the Physical Society of Japan
  • Hiroyuki Nagatani · Masayuki Oikawa

    No preview · Article · Jan 2002
  • Hidekazu Tsuji · Masayuki Oikawa
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    ABSTRACT: Oblique interaction of internal solitary waves in a two-layer fluid system with infinite depth is studied. Two-dimensional Benjamin–Ono (BO) equation is solved numerically to investigate the strong interactions of the non-linear long waves whose propagation directions are very close to each other. Computations of time development are performed for two initial settings: the first one is superposition of two BO solitons with the same amplitude and with different propagation directions, and the second one is an oblique reflection of a BO soliton at a vertical wall. It is observed that the Mach reflection does occur for small incident angles and for some incident angles very large stem waves are generated.
    No preview · Article · Oct 2001 · Fluid Dynamics Research
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    ABSTRACT: Discretization of the Bruschi-Ragnisco lattice is investegated by singularity confinement test. The equation is linearized by the Cole-Hopf like transformation.
    Preview · Article · Jan 2001

Publication Stats

405 Citations
42.35 Total Impact Points

Institutions

  • 2012
    • Fukuoka Institute of Technology
      Hukuoka, Fukuoka, Japan
  • 1993-2010
    • Kyushu University
      • Research Institute for Applied Mechanics
      Fukuoka-shi, Fukuoka-ken, Japan
  • 2009
    • University at Buffalo, The State University of New York
      Buffalo, New York, United States