• Proceedings of the Optical Society of Korea Conference
• /
• 1997.08a
• /
• pp.35-35
• /
• 1997

• Bulletin of the Society of Naval Architects of Korea
• /
• v.26 no.4
• /
• pp.3-13
• /
• 1989

In recent towing tank experiments, it has been observed that a ship moving near the critical speed $\sqrt{gh}$(g=gravitational acceleration, h=water depth) radiates solitons upstream in an almost periodic manner. As a ,consequence, the ship experiences considerable changes in resistance, trim and sinkage, or better known as squat. Mei and Choi(1987) developed a nonlinear theory for a slender ship by using the method of matched asymptotic expansions. For a certain class of channel width and ship slenderness, they found that the waves generated can be described by an inhomogeneous Korteweg-de Vries(KdV) equation. The leading-order solution properly predicts solitons propagating upstream, but it fails to render three-dimensional waves in the wake. In this paper a new approach has been made by choosing a different class of channel width and ship slenderness. The wave equation in the farfield turns out to be a homogeneous Kadomtsev-Petviashvili(KP) equation, which predicts solitons upstream and three-dimensional waves in the wake. Numerical results for the wave resistance, sinkage and trim reflect the experimentally identified phenomena.

• Kyungpook Mathematical Journal
• /
• v.57 no.4
• /
• pp.677-682
• /
• 2017

In this paper, we show that a Sasakian manifold which also satisfies the generalised gradient Ricci soliton equation, satisfying some conditions, is necessarily Einstein.

• Journal of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.81-90
• /
• 2019

We construct gradient Ricci solitons as n-dimensional submanifolds in $S^n{\times}S^n$ by using solutions of some nonlinear ODE.

• Korean Journal of Mathematics
• /
• v.28 no.4
• /
• pp.803-817
• /
• 2020

The object of the present paper is to study 𝜂-Ricci soliton on Kenmotsu manifold with respect to general connection.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.749-762
• /
• 2018

In this paper, the new optimal perturbation iteration method has been applied to solve the generalized regularized long wave equation. Comparing the new analytic approximate solutions with the known exact solutions reveals that the proposed technique is extremely accurate and effective in solving nonlinear wave equations. We also show that,unlike many other methods in literature, this method converges rapidly to exact solutions at lower order of approximations.

• Journal of applied mathematics & informatics
• /
• v.29 no.3_4
• /
• pp.847-858
• /
• 2011

We make use of the simplified Hirota's bilinear method with computer symbolic computation to study a variety of coupled potential KdV (pKdV) equations. Each coupled equation is completely integrable and gives multiple soliton solutions and multiple singular soliton solutions. The phase shifts for all coupled pKdV equations are identical whereas the coefficients of the obtained solitons are not identical. The four coupled pKdV equations are resonance free.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.3
• /
• pp.817-824
• /
• 2017

In this paper, we prove that a gradient shrinking Ricci soliton is rigid if the radial curvature vanishes and the second order divergence of Bach tensor is non-positive. Moreover, we show that a complete non-compact gradient expanding Ricci soliton is rigid if the radial curvature vanishes, the Ricci curvature is nonnegative and the second order divergence of Bach tensor is nonnegative.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.3
• /
• pp.975-992
• /
• 2017

In this article, we consider a real hypersurface of complex two-plane Grassmannians $G_2({\mathbb{C}}^{m+2})$, $m{\geq}3$, admitting commuting ${\ast}$-Ricci and pseudo anti-commuting ${\ast}$-Ricci tensor, respectively. As the applications, we prove that there do not exist ${\ast}$-Einstein metrics on Hopf hypersurfaces as well as ${\ast}$-Ricci solitons whose potential vector field is the Reeb vector field on any real hypersurfaces.

• Proceedings of the Optical Society of Korea Conference
• /
• 2003.02a
• /
• pp.310-311
• /
• 2003

비선형 Kerr 매질에서 광파의 전파 특성을 해석하기 위해 지금까지 다양한 수치해석 방법들이 연구되어오고 있다 그중 FDTD 방식은 시간의 종속적인 Maxwell curl 방정식에 대해 어떠한 시간적, 공간적 근사를 사용하지 않고 광파의 전파 특성을 시뮬레이션하기 위해 유도되었기 때문에 산란과 같은 종축방향 불연속 문제나 비종축 파의 전파 특성 문제에 대해 보다 신뢰성 있는 해석 결과를 얻을 수 있으며, 비선형 Kerr 매질에서의 광파의 전파 특성에 대해서 보다 정확한 해석이 가능하다고 알려져 있다. (중략)