• Kyungpook Mathematical Journal
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• 제49권1호
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• pp.81-93
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• 2009

Bifurcation method of dynamical systems is employed to investigate exact solitary wave solutions and kink wave solutions in the generalized modified Boussinesq equation. Under some parameter conditions, their explicit expressions are obtained. Some previous results are extended.

• 충청수학회지
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• 제24권2호
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• pp.359-370
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• 2011

In this work, we obtain new solitary wave solutions for some nonlinear partial differential equations. The Jacobi elliptic function rational expansion method is used to establish new solitary wave solutions for the combined KdV-mKdV and Klein-Gordon equations. The results reveal that Jacobi elliptic function rational expansion method is very effective and powerful tool for solving nonlinear evolution equations arising in mathematical physics.

• 호남수학학술지
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• 제33권2호
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• pp.247-259
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• 2011

In this paper, the $(\frac{G'}{G})$-expansion method is used to construct new exact travelling wave solutions of some nonlinear evolution equations. The travelling wave solutions in general form are expressed by the hyperbolic functions, the trigonometric functions and the rational functions, as a result many previously known solitary waves are recovered as special cases. The $(\frac{G'}{G})$-expansion method is direct, concise, and effective, and can be applied to man other nonlinear evolution equations arising in mathematical physics.

• Journal of Astronomy and Space Sciences
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• 제23권3호
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• pp.209-216
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• 2006

Ion acoustic solitary wave in a plasma consisting of electrons and ions with an external magnetic field is reinvestigated using the Sagdeev's potential method. Although the Sagdeev potential has a singularity for n < 1, where n is the ion number density, we obtain new solitary wave solutions by expanding the Sagdeev potential up to ${\delta}n^4$ near n = 1. They are compressiv (rarefactive) waves and shock type solitary waves. These waves can exist all together as a superposed wave which may be used to explain what would be observed in the solar wind plasma. We compared our theoretical results with the data of the Freja satellite in the study of Wu et al. (1996). Also it is shown that these solitary waves propagate with a subsonic speed.

• 대한수학회논문집
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• 제35권2호
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• pp.685-695
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• 2020

In this paper, we used modified tanh-coth method, combined with Riccati equation and secant hyperbolic ansatz to construct abundantly many real and complex exact travelling wave solutions to KdV-Burgers (KdVB) equation with forcing term. The real part is the sum of the shock wave solution of a Burgers equation and the solitary wave solution of a KdV equation with forcing term, while the imaginary part is the product of a shock wave solution of Burgers with a solitary wave travelling solution of KdV equation. The method gives more solutions than the previous methods.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.143-152
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• 2010

Based on the Exp-function method and a suitable transformation, new generalized solitonary solutions including free parameters of the MDI and Sawada-Kotera equations with variable coefficients are obtained, form which solitary wave solutions and periodic solutions including some known solutions reported in open literature are derived as special cases. The free parameters in the obtained generalized solitonary solutions might imply some meaningful results in the physical models. It is shown that the Exp-function method provides a very effective and important new method for nonlinear evolution equations with variable coefficients.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.197-208
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• 2006

This paper deals with the exact solution of surface gravity waves in an ocean with irregular bed topography. In order to obtain water surface elevation and run-up of infra-gravity waves when the bed is either wavy or exponential, closed form solutions are obtained. Numerical computations indicate that when solitary wave or sinusoidal wave conditions are applied at the boundary, water surface elevation attains near Gaussian profile.

• 물과 미래
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• 제28권6호
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• pp.159-168
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• 1995

본 논문에서는 2차원 경계요소법 수치모형을 이용하여 급경사에서 고립파의 처오름과 진행과정을 연구하였다. 먼저 수치모형을 상대적으로 완만한 경사에 적용하여 처오름 높이를 산정하여 기존의 수리모형실험의 결과, 수치해 및 해석해 등과 비교하여 수치모형의 정확도를 검증하였다. 경계요소법에 의한 수치해는 전체적으로 기존의 자료 등과 잘 일치하였다. 다음에 수치모형을 급경사 지형에 적용하여 처오름 높이를 산정한다. 경계요소법은 완경사 뿐만 아니라 급경사에서도 고립파의 최대 처오름 높이 산정에 매우 효율적이며, 경계요소법에 의한 결과는 인공수로의 제방 또는 방파제의 설계에 이용될 수 있을 것이다. 마지막으로, 급경사에서의 고립파의 파고를 계산하여 Green의 법칙에 의한 결과와 비교하였다.

• 대한수학회지
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• 제37권6호
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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.

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.119-130
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• 2002

An extended Jacobin elliptic function method is presented for constructing exact travelling wave solutions of nonlinear partial differential equations(PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation that Jacobin elliptic functions satisfy and use its solutions to replace Jacobin elliptic functions in Jacobin elliptic function method. It is interesting that many other methods are special cases of our method. Some illustrative equations are investigated by this means.