A Modified Reductive Perturbation Method as Applied to Nonlinear Ion-Acoustic Waves

Demı́ray, Hilmi

doi:10.1143/jpsj.68.1833

Cited by 25 publications

(35 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is shown that the wave speed corresponding to the lowest order time parameter r gives the wave speed of the classical perturbation expansion, whereas the wave speeds corresponding to higher order time parameters give the speed corrections terms. The results obtained here are exactly the same as those given in Malfliet and Wieers [6] and Demiray [7],…”

Section: Introductionsupporting

confidence: 90%

“…This requirement made it possible to remove the secularities that might occur and to determine the higher order correction terms to the wave speed. The result obtained in [7] was found to be in complete agreement with that of Malfliet and Wieers [6].…”

Section: Introductionsupporting

confidence: 87%

“…A particular solution to equations (33) and (34) takes the form: This result is exactly the same as those obtained by Malfliet and Wieers [6] and Demiray [7], The present derivation can be reduced to the modified reductive perturbation method presented in [7] by introducing the …”

Section: Solitary Wavessupporting

confidence: 76%

“…Another attempt to remove this uncertainty was made by Demiray [7] who modified the conventional reductive perturbation method by introducing a scaling parameter and expanding it into a power series of the same smallness parameter and balancing higher order nonlinearity with higher order dispersive effect. This requirement made it possible to remove the secularities that might occur and to determine the higher order correction terms to the wave speed.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multiple - scale Expansion for Nonlinear Ion-acoustic Waves

Demı́ray¹

2010

International Journal of Nonlinear Sciences and Numerical Simulation

View full text Add to dashboard Cite

By employing the multiple-scale expansion method, the present work examines non-linear waves in a cold collisionless plasma, in the long-wave limit, and obtains a set of KdV equations governing various order terms in the perturbation expansion. By seeking a travelling wave type of solution to the evolution equations, a set of wave speeds associated with each time parameter are obtained. It is shown that the speed corresponding to the lowest order time parameter gives the wave speed of the conventional reductive perturbation method. The speeds corresponding to the higher order time parameters give the correction terms to the wave speeds of the classical reductive perturbation method.

show abstract

Section: Introductionsupporting

confidence: 90%

Section: Introductionsupporting

confidence: 87%

Section: Solitary Wavessupporting

confidence: 76%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multiple - scale Expansion for Nonlinear Ion-acoustic Waves

Demı́ray¹

2010

International Journal of Nonlinear Sciences and Numerical Simulation

View full text Add to dashboard Cite

show abstract

“…For this we adopt the long wave approximation and employ the modified reductive perturbation method, the details of which are given by Demiray [16].…”

Section: Long Wave Approximationmentioning

confidence: 99%

The Effects of Higher-Order Approximations in a Fluid-Filled Elastic Tube with Stenosis

Demı́ray

2006

Zeitschrift Für Naturforschung A

View full text Add to dashboard Cite

Treating arteries as thin-walled prestressed elastic tubes with a narrowing (stenosis) and blood as an inviscid fluid, we study the propagation of weakly nonlinear waves in such a fluid-filled elastic tube by employing the reductive perturbation method in the long wave approximation. It is shown that the evolution equation of the first-order term in the perturbation expansion may be described by the conventional Korteweg-de Vries (KdV) equation. The evolution equation for the second-order term is found to be the linearized KdV equation with a nonhomogeneous term, which contains the contribution of the stenosis. A progressive wave type solution is sought for the evolution equation, and it is observed that the wave speed is variable, which results from the stenosis. We study the variation of the wave speed with the distance parameter τ for various amplitude values of the stenosis. It is observed that near the center of the stenosis the wave speed decreases with increasing stenosis amplitude. However, sufficiently far from the center of the stenosis stenosis amplitude becomes negligibly small.

show abstract

Contribution of higher order terms in electron-acoustic solitary waves with vortex electron distribution

Demı́ray

2014

Z. Angew. Math. Phys.

View full text Add to dashboard Cite

A Modified Reductive Perturbation Method as Applied to Nonlinear Ion-Acoustic Waves

Cited by 25 publications

References 6 publications

Multiple - scale Expansion for Nonlinear Ion-acoustic Waves

Multiple - scale Expansion for Nonlinear Ion-acoustic Waves

The Effects of Higher-Order Approximations in a Fluid-Filled Elastic Tube with Stenosis

Contribution of higher order terms in electron-acoustic solitary waves with vortex electron distribution

Contact Info

Product

Resources

About