• Honam Mathematical Journal
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• v.39 no.4
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• pp.649-654
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• 2017

In this note, we seek traveling wave solutions of a shallow water model in a one dimensional space by a simple but rigorous calculation. From the profile equation of traveling wave solutions, we need to investigate the phase portrait of a one dimensional ordinary differential equation $\tilde{u}^{\prime}=F(\tilde{u})$ connecting two end states of the traveling wave solution.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.261-273
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• 2015

We consider the hyperelastic rod equation describing nonlinear dispersive waves in compressible hyperelastic rods. We investigate the existence of certain traveling wave solutions to this equation. We also determine whether two other equations(the b-family equation and the modified Camassa-Holm equation) have our solution type.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1431-1437
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• 2010

We use the (G'/G)-expansion method to seek the traveling wave solution of the Seventh-order Sawada-Kotera Equation. The solutions that we get are more general than the solutions given in literature. It is shown that the (G'/G)-expansion method provides a very effective and powerful mathematical tool for solving nonlinear equations in mathematical physics.

• Journal of international Conference on Electrical Machines and Systems
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• v.3 no.1
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• pp.32-39
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• 2014

Traveling wave generation in a ring type stator has been studied. The basic working principle to create traveling wave has been modelled by the superposition of two orthogonal standing waves. Theoretical analysis shows that the length to radius ratio affects the frequency gap between two pseudo orthogonal modes used to create traveling wave. FEM simulation is then discussed and applied to validate the analytical model. At last, a possible optimal solution is reported with FEM verification.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.635-646
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• 2012

This paper is concerned with an SIRS epidemic model with spatial diffusion and time delay representing the length of the immunity period. By using a new cross iteration scheme and Schauder's fixed point theorem, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a newfashioned pair of upper-lower solutions, we derive the existence of a traveling wave solution connecting the uninfected steady state and the infected steady state.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.27-40
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• 2017

In this paper, we construct exact traveling wave solutions of various kind of partial differential equations arising in mathematical science by the system technique. Further, the $Painlev{\acute{e}}$ test is employed to investigate the integrability of the considered equations. In particular, we describe the behaviors of the obtained solutions under certain constraints.

• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.141-154
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• 2023

We study the stability of traveling waves of a certain chemotaxis model. The traveling wave solution is a central object of study in a chemotaxis model. Kim et al. [8] introduced a model on a population and nutrient densities based on a nonlinear diffusion law. They proved the existence of traveling waves for the one dimensional Cauchy problem. Existence theory for traveling waves is typically followed by stability analysis because any traveling waves that are not robust against a small perturbation would have little physical significance. We conduct a numerical nonlinear stability for a few relevant instances of traveling waves shown to exist in [8]. Results against absolute additive noises and relative additive noises are presented.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.73-80
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• 2006

In order to examine the validity of an asymptotic solution for nonlinear interaction in asymmetric vibration modes of a perfect circular plate, we obtain the numerical solution. The motion of the plate is governed by nonlinear partial differential equation. The initial and boundary value problem is solved by using the finite difference method. The numerical solution is compared with the asymptotic solution. It is found that traveling waves relating clockwise and counterclockwise as well as standing wave are depicted by the numerical solution.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.2
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• pp.96-110
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• 1995

Traveling-wave electrodes for the high-speed Ti:LiNbO$_{3}$ modulators are designed. For a solution to the problems of 1) phase-velocity mismatching between the optical wave and the Modulating M/W, 2) M/W electrode characteristic impedance mismateching, we assume devices with 1$\mu$m thick SiO$_{2}$ buffer layer between the electrode and the Ti:LiNbO$_{3}$ substrate. The electrode analyses are performed by the FEM using the second-order triangular elements. The optimum design parameters to satisfy the phase-velocity matching and the characteristic impedance matching are sought for. By use of the analyses' results, a Mach-Zehnder optical modulator with a CPW electrode is designed as an example. the band-width estimation is also illustrated.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.369-380
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• 2011

This paper studies a boundary value problem for a linear coupled Luikov's system of heat and mass diffusion in one-dimensional case. Using an a priori estimate, we prove the uniqueness of the solution. Also, some traveling wave solutions and explicit solutions are obtained by using the transformation ${\xi}$ = x - ct and separation method respectively.