Publications (47)42.35 Total impact
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ABSTRACT: Solitary waves are typical nonlinear long waves in the ocean. The twodimensional interaction of solitary waves has been shown to be essentially different from the onedimensional case and can be related to generation of large amplitude waves (including 'freak waves'). Concerning surfacewater waves, Miles (1977) theoretically analyzed interaction of three solitary waves, which is called "resonant interaction" because of the relation among parameters of each wave. Weaklynonlinear numerical study (Funakoshi, 1980) and fullynonlinear 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. 
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Article: Large Amplitude Internal Solitary Waves due to Solitary Resonance regarding the Change in Amplitude
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ABSTRACT: To clarify the resonance of fullynonlinear internal solitary waves which is one of the reasons for the occurrence of large amplitude internal waves, fullynonlinear and stronglydispersive internal wave equation model was applied, which attempted to investigate interaction of internal solitary waves in a twodimensional plane. The 3rd order theoretical solutions for internal waves in a twolayer 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.  [Show abstract] [Hide abstract]
ABSTRACT: Twodimensional (2D) interactions of two interfacial solitons in a twolayer 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 integropartial differential equation that we call the twodimensional ILW (2DILW) equation. By solving it numerically for a Vshaped 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 twodimensional Benjamin–Ono (2DBO) equation. 
Article: Nonlinear Characteristics of Internal Waves in a DeepWater Region or near a WaveBreaking Point
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ABSTRACT: A set of nonlinear internalwave 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 deepwater 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 wavebreaking point. In the wavebreaking 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.  [Show abstract] [Hide abstract]
ABSTRACT: Applicability of the 3rd order theoretical solutions for internal waves in a twolayer 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.  [Show abstract] [Hide abstract]
ABSTRACT: We consider the initial value problems of the KadomtsevPetviashvili (KP) equation for symmetric Vshape initial waves consisting of two semiinfinite 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.  [Show abstract] [Hide abstract]
ABSTRACT: We study the maximum wave amplitude produced by linesoliton interactions of the KadomtsevPetviashvili II (KPII) equation, and we discuss a mechanism of generation of large amplitude shallow water waves by multisoliton 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 multisoliton complexes of the KPII equation which verify the robustness of all types of soliton interactions and weblike 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 
Article: Note on the 2component Analogue of 2dimensional Long WaveShort Wave Resonance Interaction System
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ABSTRACT: An integrable twocomponent analogue of the twodimensional long waveshort wave resonance interaction (2c2dLSRI) system is studied. Wronskian solutions of 2c2dLSRI 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. 
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ABSTRACT: Oblique interaction of two solitons of the same amplitude in an extended KadomtsevPetviashvili (EKP) equation, which is a weakly twodimensional generalization of an extended Kortewegde 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 KadomtsevPetviashvili 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.  [Show abstract] [Hide abstract]
ABSTRACT: We consider a mechanism of generation of huge waves by multisoliton resonant interactions. A nonstationary wave amplification phenomenon is found in some exact solutions of the KadomtsevPetviashvili (KP) equation. The mechanism proposed here explains the character of extreme waves and of those in Tsunami.  [Show abstract] [Hide abstract]
ABSTRACT: The twocomponent analogue of twodimensional long waveshort wave resonance interaction equations is derived in a physical setting. Wronskian solutions of the integrable twocomponent analogue of twodimensional long waveshort 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  [Show abstract] [Hide abstract]
ABSTRACT: Studies on the oblique interactions of weakly nonlinear long waves in dispersive systems are surveyed. We focus mainly our concentration on the twodimensional interaction between solitary waves. Twodimensional 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 largeamplitude 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 KPII equation. Recent studies on exact solutions of the KP equation are also surveyed briefly.  [Show abstract] [Hide abstract]
ABSTRACT: It is shown that generation of the rogue waves in the ocean may be described in framework of nonlinear twodimensional shallow water theory where the simplest twodimensional long wave nonlinear 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 noninteracting longcrested waves. Peculiarities of the solution allow to explain rare and unexpected appearance of the rogue waves. However, our solution differs from the exact twosolitary wave solution of the KP equation used before for the rogue waves description. 
Article: Twodimensional Interaction of Solitary Waves in a Modified KadomtsevPetviashvili Equation
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ABSTRACT: Twodimensional interaction of two solitary waves is investigated numerically on the basis of a Modified KadomtsevPetviashvili 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. 
Article: Generalized Casorati Determinant and PositonNegatonType Solutions of the Toda Lattice Equation
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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. 
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ABSTRACT: Oblique interaction of internal solitary waves in a twolayer fluid system with infinite depth is studied. Twodimensional Benjamin–Ono (BO) equation is solved numerically to investigate the strong interactions of the nonlinear 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.  [Show abstract] [Hide abstract]
ABSTRACT: Discretization of the BruschiRagnisco lattice is investegated by singularity confinement test. The equation is linearized by the ColeHopf like transformation.
Publication Stats
405  Citations  
42.35  Total Impact Points  
Top Journals
Institutions

2012

Fukuoka Institute of Technology
Hukuoka, Fukuoka, Japan


19932010

Kyushu University
 Research Institute for Applied Mechanics
Fukuokashi, Fukuokaken, Japan


2009

University at Buffalo, The State University of New York
Buffalo, New York, United States
