• Journal of Ocean Engineering and Technology
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• v.13 no.2 s.32
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• pp.116-128
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• 1999

A deep water wave prediction model applicable to the East Sea is presnted. This model incorporates rediative transter of energy specrum, atmospheric input form the wind, nonlinear interaction, and energy dissipation by white capping. The propagation scheme by Gadd shows satisfactory results and the characteristics of the nonlinear interaction is simulated well by discrete interaction approximatiion. The application of the model to the sea around the Korean Peninsula shows reasonable agreement with the observation.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.153-167
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• 1996

In this paper we investigate the existence of solutions of a nonlinear wave equation $u_{tt} - u_{xx} = p(x, t, u)$$ in $H_0$, where $H_0$ is the Hilbert space spanned by eigenfunctions. If p satisfy condition $(p_1) - (p_3)$, this nonlinear gave equation has at least one solution.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1161-1178
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• 2018

In this paper, we consider the Cauchy problem for a class of nonlinear sixth-order wave equation. The global existence and the finite time blow-up for the problem are proved by the potential well method at both low and critical initial energy levels. Furthermore, we present some sufficient conditions on initial data such that the weak solution exists globally at supercritical initial energy level by introducing a new stable set.

• Proceedings of the Optical Society of Korea Conference
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• 2003.02a
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• pp.42-43
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• 2003

The nonlinear three-wave interaction is an interesting topic having various applications in nonlinear optics, hydrodynamics, acoustic waves, and plasma physics. The resonant interaction between two laser pulses and a plasma wave plays important roles in plasma heating, laser reflection in the inertial confinement fusion (ICF), plasma wakefield generation, and ultra-intense laser pulse amplification and pulse compression using stimulated Raman backscattering (RBS). (omitted)

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.205-216
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• 2022

This paper deals with a nonlinear wave equation with boundary damping and source terms of variable exponent nonlinearities. This work is devoted to prove a global nonexistence of solutions for a nonlinear wave equation with nonnegative initial energy as well as negative initial energy.

• Proceedings of the Acoustical Society of Korea Conference
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• spring
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• pp.347-348
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• 2004

Nonlinear scattering of difference frequency acoustic wave in a water-saturated sandy sediment was investigated. Difference frequency acoustic wave was observed to be scattered due to the nonlinearity of water-saturated sandy sediment when the collinear acoustic waves with two different fundamental frequencies are incident on the sediment. The pressure level of the difference frequency acoustic wave was 6 dB higher than the background noise level. It seems very useful to evaluate the nonlinear parameter of water-saturated sandy sediment without disturbing the sediment. Such nonlinear acoustic response of water-saturated sandy sediment can be used as background acoustic data for estimating the gas void fraction in marine gassy sandy sedimen.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.5 no.4
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• pp.307-317
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• 1993

The problem of sea wave transformation in the coastal zone taking into account effects of nonlinearity and disperison has been studied. Mathematical model for description of regular wave transformation is based on the method of nonlinear ray theory. The equations for rays and wave field have been produced. Nonlinear wave field is described by the modified Korteweg-de Vries equation. Some analytical solutions of this equation are obtained. Caustic transformation and dissipation effects are included in the mathematical model. Numerical algorithm of solution of the Korteweg-de Vries equation and its stability criterion are described. Results of nonlinear transformation of sea waves in the coastal zone are demonstrated.

• Journal of Ocean Engineering and Technology
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• v.12 no.2 s.28
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• pp.33-42
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• 1998

In the presence of incident waves with different frequencies, the second order sum and difference frequency waves due to the nonlinearity of the incident waves come into existence. Although the magnitudes of the forces produced on a Tension Leg Platform(TLP) by these nonlinear waves are small, they act on the TLP at sum and difference frequencies away from those of the incident waves. So, the second order sum and difference frequency wave loads produced close to the natural frequencies of TLPs often give greater contributions to high and low frequency resonant responses. The second order wave exciting forces and moments have been obtained by the method based on direct integration of pressure acting on the submerged surface of a TLP. The components of the second order forces which depend on first order quantities have been evaluated using the three dimensional source distribution method. The numerical results of time domain analysis for the nonlinear wave exciting forces in regular waves are compared with the numerical ones of frequency domain analysis. The results of comparison confirmed the validity of the proposed approach.

• The Journal of the Acoustical Society of Korea
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• v.22 no.4
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• pp.250-260
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• 2003

Since a bubble in water is a highly nonlinear acoustic scatterer, the acoustic scattered waves from underwater bubbles show highly nonlinear acoustic properties. These acoustic scattered waves can be observed at the second or higher harmonics as well as at the fundamental primary frequency of incident acoustic wave. When two primary acoustic waves of different frequencies are incident on a bubble, the acoustic scattered waves can be also observed at the sum and the difference frequencies of the primary waves. In this study, when the two primary acoustic waves were incident on a bubble screen in water, we observed that the amplitude of difference frequency wave was amplified by the bubble nonlinearity and its directivity was oriented in the propagation directions of primary waves. The directivity of scattered difference frequency wave was analyzed as a coherent scattering for virtual source by using the directivity of the primary acoustic wave.

• Journal of Ocean Engineering and Technology
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• v.11 no.4
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• pp.111-121
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• 1997

The spectral energy balance model is composed and the nonlinear interaction is approximated by the discrete interaction parameterization as in WAM model. The numerical results of durational limited growth test agree very well with those of the exact model, EXACT-NL. The response of a wave spectrum to a change in wind direction is investigated numerically for a sequence of direction changes 30$^{\circ}$ , 45$^{\circ}$ , 60$^{\circ}$ , 90$^{\circ}$ . The high frequency components relax more repidly to the new wind direction than the low frequency components and the relaxation process also depends on the wave age. For wind direction changes less than 60$^{\circ}$ , the coupling by nonlinear interaction is so strong that the secondary peak in input source distribution is counteracted by the negative lobe of the nonlinear interaction. For wind direction changes grater than 60$^{\circ}$ , a second independent wind-sea spectrum is generated in the new wind direction, while the old spectrum gradually decays as swell.