• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.977-989
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• 2000

In this paper we construct a standing solitary wave solution with prescribed total electric charge to the planer Chern-Simons gauged nonlinear Schrodinger equation with an external electromagnetic field by using a variations method.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.75-85
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• 2005

In this paper, the visco-Da-Rios equation; (0.1) ($$\frac{{\partial}{\gamma}}{{\partial}t}=\frac{{\partial}{\gamma}}{{\partial}s}{\bigwedge}\frac{D}{ds}\frac{{\partial}{\gamma}}{{\partial}s}+{\nu}\frac{{\partial}{\gamma}}{{\partial}s}$$) is investigated on 3-dimensional complete orientable Riemannian manifolds. The global existence of solution is discussed by trans-forming (0.1) into a cubic nonlinear Schrodinger equation for complete orient able Riemannian 3-manifolds of constant curvature.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.683-691
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• 2001

A linearized finite-difference scheme is used to transform the initial/boundary-value problem associated with the nonlinear Schrodinger equation into a linear algebraic system. This method is developed by replacing the time and the nonlinear term by an appropriate parametric linearized scheme based on Taylor’s expansion. The resulting finite-difference method is analysed for stability and convergence. The results of a number of numerical experiments for the single-soliton wave are given.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.337-348
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• 2001

The unitary Lie-Trotter-Kato product formula gives in a simplest way a meaning to the Feynman path integral for the Schroding-er equation. In this note we want to survey some of recent results on the norm convergence of the selfadjoint Lie-Trotter Kato product formula for the Schrodinger operator -1/2Δ + V(x) and for the sum of two selfadjoint operators A and B. As one of the applications, a remark is mentioned about an approximation therewith to the fundamental solution for the imaginary-time Schrodinger equation.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.4 no.3
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• pp.156-160
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• 1992

The evolution of leading waves generated by a wavemaker in a two-dimensional tank has been studied. The front of wave trains can be described in general by the Schrodinger equation. In particular, when the slope of the carrier waves is steep, and hence nonlinearity becomes important, the cubic Schrodinger equation is proved to be an appropriate mathematical model. Computations are made by using the Crank-Nicolson algorithm and compared with experimental data. It is found that the numerical result predicts the evolution of leading waves fairly well and the evolution is significantly affected by nonlinearity for steep waves when kh＞1.36.

• East Asian mathematical journal
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• v.35 no.1
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• pp.1-7
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• 2019

We consider the initial value problem of the Schrodinger equation for an interesting Cauchy-Euler type operator ${\mathfrak{R}}$ on ${\mathbb{C}}^n$ that is an analogue of the harmonic oscillator in ${\mathbb{R}}^n$. We get an appropriate $L^1-L^{\infty}$ dispersive estimate for the solution of the initial value problem.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.469-483
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• 2001

The configuration space and phase space oscillatory path integrals are computed in the case of the stochastic Schrodinger equation for the harmonic oscillator with a stochastic term of the form (K$\psi$(sub)t)(x) o dW(sub)t, where K is either the position operator or the momentum operator, and W(sub)t is the Wiener process. In this way formulae are derived for the stochastic analogues of the Mehler kernel.

• Proceedings of the IEEK Conference
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• 1999.11a
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• pp.917-920
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• 1999

Modal transmission-line theory is described for guided electron waves in quantum-well structures. To demonstrate the validity and usefulness of this approach, we evaluate the propagation characteristics and the coupling properties of electron guiding couplers consisting of double quantum-wells (DQWs).

• Bulletin of the Korean Chemical Society
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• v.17 no.2
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• pp.188-192
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• 1996

It is shown that the inversion of the undamped Bloch equation for an amplitude-modulated broadband π/2 pulse can be precisely treated as an inverse scattering problem for a Schrodinger equation on the positive semiaxis. The pulse envelope is closely related to the central potential and asymptotically the wave function takes the form of a regular solution of the radial Schrodinger equation for s-wave scattering. An integral equation, which allows the calculation of the pulse amplitude (the potential) from the phase shift of the asymptotic solution, is derived. An exact analytical inversion of the integral equation shows that the detuning-independent π/2 pulse amplitude is given by a delta function. The equation also provides a means to calculate numerically approximate π/2 pulses for broadband excitation.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.33A no.7
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• pp.223-229
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• 1996

a simpel coordinate transformaton method is suggested that converts Schr$\"{o}$dinger's equation involving a position-dependent effective mass in a heterostructure to an equation involving a positon-independent effective mass. This method enables the conceptual study of the effect of the positon-dependent effective mass inserted between the divergence operator and the gradient operator in Schr$\"{o}$dinger's equation. It is also shown that the characteristics such as a transmission coefficient in various heterostructures involving a position-dependent effective masses can be obtained iwth ease by the suggested method.