• Honam Mathematical Journal
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• v.43 no.4
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• pp.613-626
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• 2021

The aim of the present work is to study the properties of three-dimensional Lorentzian para-Kenmotsu manifolds equipped with a Yamabe soliton. It is proved that every three-dimensional Lorentzian para-Kenmotsu manifold is Ricci semi-symmetric if and only if it is Einstein. Also, if the metric of a three-dimensional semi-symmetric Lorentzian para-Kenmotsu manifold is a Yamabe soliton, then the soliton is shrinking and the flow vector field is Killing. We also study the properties of three-dimensional Ricci symmetric and 𝜂-parallel Lorentzian para-Kenmotsu manifolds with Yamabe solitons. Finally, we give a non-trivial example of three-dimensional Lorentzian para-Kenmotsu manifold.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.479-492
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• 2024

In this paper, we study Riemannian submersions whose total manifold admits h-almost Ricci-Yamabe soliton. We characterize the fibers of the submersion and see under what conditions the fibers form h-almost Ricci-Yamabe soliton. Moreover, we find the necessary condition for the base manifold to be an h-almost Ricci-Yamabe soliton and Einstein manifold. Later, we compute scalar curvature of the total manifold and using this we find the necessary condition for h-almost Yamabe solition to be shrinking, expanding and steady. At the end, we give a non-trivial example.

• Korean Journal of Optics and Photonics
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• v.12 no.1
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• pp.48-54
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• 2001

We investigate the generation of the dark spatial soliton and its role of wave guiding in Fe doped$LiNbO_3$ A cw Ar+ laser of 488 nm is used for the generation of the dark spatial soliton. The generation of the dark spatial soliton is observed even at the laser intensity as low as 10 mW/cm2. The self-defocusing effect is observed when the direction of the intensity variation is parallel to the optic axis, while it can't be seen when perpendicular to the axis. So, it is verified that the refractive index change is generated parallel to the optic axis. When 633 nm He-Ne laser beam is injected into the dark spatial soliton, the beam propagates just as in the diffraction free medium. So, it is verified that the dark spatial soliton can act as a waveguide.eguide.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.7
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• pp.1191-1202
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• 1994

We numerically investigate a stable propagation regime of soliton pulse trains in fibers with periodically copensated loss by lumped optical amplifiers. When amplification solition pulses is 1.2~1.5 and the minimum soliton separation normalized by the soliton width becomes about 6. In cases of L=50[km], the allowable range of A is 1.5~1.7 under =6. The maximum allowable variation of the loss compensation in each lumped amplifier becomes +-2% of the fiber loss when L=50[km], A=1.6, and =6. Generally, the allowable rages of the soliton amplitude A and amplifier gain are inversely proportional to the amplification period L.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.213-219
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• 2014

We prove that a semi-symmetric 3-dimensional gradient Ricci soliton is locally isometric to a space form $\mathbb{S}^3$, $\mathbb{H}^3$, $\mathbb{R}^3$ (Gaussian soliton); or a product space $\mathbb{R}{\times}\mathbb{S}^2$, $\mathbb{R}{\times}\mathbb{H}^2$, where the potential function depends only on the nullity.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.847-858
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• 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
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• v.54 no.3
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• pp.817-824
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• 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.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.539-552
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• 2020

In this paper we consider gradient almost Ricci solitons with weak conditions on Weyl and Bach tensors. We show that a gradient almost Ricci soliton has harmonic Weyl curvature if it has fourth order divergence-free Weyl tensor, or it has divergence-free Bach tensor. Furthermore, if its Weyl tensor is radially flat, we prove such a gradient almost Ricci soliton is locally a warped product with Einstein fibers. Finally, we prove a rigidity result on compact gradient almost Ricci solitons satisfying an integral condition.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.219-226
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• 2020

In this paper, we consider gradient Ricci solitons and gradient Yamabe solitons in the warped product spaces. Also we study warped product space with harmonic curvature related to gradient Ricci solitons and gradient Yamabe solitons. Consequently some theorems are generalized and we derive differential equations for a warped product space to be a gradient Ricci soliton.

• Journal of the Optical Society of Korea
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• v.3 no.1
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• pp.20-22
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• 1999

We present numerically simulated results on stabilities of optical soliton transmission in highly-dispersion-perturbed optical fiber systems. We have found that the perturbation of dispersion along the transmission line does not significantly degrade stability of soliton transmission as long as the average soliton concept is obeyed.