Masayuki Oikawa

Kyushu University, Fukuoka-shi, Fukuoka-ken, Japan

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Publications (42)43.85 Total impact

  • Coastal Engineering Proceedings. 12/2012; 1(33).
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    Dataset: Correction
  • 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.
    Fluid Dynamics Research 10/2010; 42(6):065506. · 0.76 Impact Factor
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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
    Studies in Applied Mathematics 03/2009; · 1.31 Impact Factor
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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. Those are particularly important for studies of large amplitude waves such as tsunami in shallow water. Numerical simulations show that the solutions of the initial value problem approach asymptotically to certain exact solutions of the KP equation found recently in [1]. We then use a chord diagram to explain the asymptotic result. This provides an analytical method to study asymptotic behavior for the initial value problem of the KP equation. We also demonstrate a real experiment of shallow water waves which may represent the solution discussed in this communication.
    Journal of Physics A Mathematical and Theoretical 01/2009; 42(31). · 1.77 Impact Factor
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    ABSTRACT: The numeric values in the index pairs of [Stud. Appl. Math. 122, No. 4, 377–394 (2009; Zbl 1172.35475)] are corrected.
    Studies in Applied Mathematics 01/2009; 123(4). · 1.31 Impact Factor
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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.
    Glasgow Mathematical Journal 01/2009; 51. · 0.44 Impact Factor
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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.
    03/2007;
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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
    Journal of Physics A Mathematical and Theoretical 02/2007; · 1.77 Impact Factor
  • 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.
    Journal of the Physical Society of Japan 01/2007; 76(8). · 2.09 Impact Factor
  • 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.
    Fluid Dynamics Research 01/2006; · 0.76 Impact Factor
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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.
    Wave Motion 09/2005; · 1.47 Impact Factor
  • 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.
    Journal of the Physical Society of Japan 11/2004; 73(11):3034-3043. · 2.09 Impact Factor
  • 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.
    Journal of the Physical Society of Japan 01/2004; 73(4):831-837. · 2.09 Impact Factor
  • Hiroyuki Nagatani, Masayuki Oikawa
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    ABSTRACT: The Rayleigh-Benard convection near onset under free-free boundary conditions for a small Prandtl number and a large aspect ratio is studied. In this case, a direct transition from conduction to spatiotemporal chaos has been reported. We solve numerically the generalized Swift-Hohenberg equations proposed by Manneville for a fluid of Prandtl number Pr=0·5 and the aspect ratio γ=60. We investigate similarities and differences between the results of the three-dimensional numerical simulation of the Boussinesq fluid for the same condition performed by Xi, Li and Gunton and those obtained from the Manneville model.
    Engineering Sciences Reports. 01/2002; 24(3).
  • 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.
    Fluid Dynamics Research 10/2001; · 0.76 Impact Factor
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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.
    01/2001;
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    Ken-ichi Maruno, Masayuki Oikawa
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    ABSTRACT: The relativistic Lotka–Volterra (RLV) lattice and the discrete-time relativistic Lotka–Volterra (dRLV) lattice are investigated by using the bilinear formalism. The bilinear equations for them are systematically constructed with the aid of the singularity confinement test. It is shown that the RLV lattice and dRLV lattice are decomposed into the Bäcklund transformations of the Toda lattice system. The N-soliton solutions are explicitly constructed in the form of the Casorati determinant.
    Physics Letters A 01/2000; 270:122-131. · 1.63 Impact Factor
  • Kenji Kajiwara, Ken-Ichi Maruno, Masayuki Oikawa
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    ABSTRACT: An elementary and systematic method to construct exact solutions for discrete soliton equations is presented. In this method, the singularity patterns, obtained through the singularity confinement test, give us critical information for bilinearization.
    Chaos Solitons & Fractals 01/2000; 11(1):33-39. · 1.50 Impact Factor
  • Hidekazu Tsuji, Masayuki Oikawa
    RIMS Kokyuroku. 01/1999;

Publication Stats

244 Citations
43.85 Total Impact Points

Institutions

  • 1996–2010
    • Kyushu University
      • Research Institute for Applied Mechanics
      Fukuoka-shi, Fukuoka-ken, Japan
    • Ryukoku University
      Kioto, Kyōto, Japan
  • 2005
    • Arctic and Antarctic Research Institute
      Sankt-Peterburg, St.-Petersburg, Russia