Weakly nonlinear waves in a prestressed thin elastic tube containing a viscous fluid

Antar, Nalan; Demı́ray, Hilmi

doi:10.1016/s0020-7225(98)00148-7

Cited by 22 publications

(18 citation statements)

References 18 publications

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“…They arise in many nonlinear problems such as water waves, [13][14][15][16][17] waves in plasmas, [18][19][20][21][22][23] nonlinear waves in fluid-filled elastic or viscoelastic tubes, [24][25][26] and other nonlinear waves of similar nature.…”

Section: Introductionmentioning

confidence: 99%

Modulation of electron-acoustic waves in a plasma with kappa distribution

Demı́ray

2016

Physics of Plasmas

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In the present work, employing a one dimensional model of an unmagnetized collisionless plasma consisting of a cold electron fluid, hot electrons obeying j velocity distribution, and stationary ions, we study the amplitude modulation of an electron-acoustic waves by use of the conventional reductive perturbation method. Employing the field equations of such a plasma, we obtained the nonlinear Schr€ odinger equation as the evolution equation. Seeking a harmonic wave solution with progressive wave amplitude to the evolution equation, as opposed to the plasma with vortex distribution, the amplitude wave assumes a shock wave type of solution. Finally, the modulational stability of the wave is studied and it is observed that the wave is modulationally stable for all admissible wave numbers. V C 2016 AIP Publishing LLC. [http://dx

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Section: Introductionmentioning

confidence: 99%

Modulation of electron-acoustic waves in a plasma with kappa distribution

Demı́ray

2016

Physics of Plasmas

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“…Thus, when small but finite amplitude travelling waves are considered in the long wavelength limit, we expect to see the famous KdV equation, or KdV-Burgers equation if viscous effects are taken into account, to emerge as the evolution equation for the wave amplitude. There now exists a good number of papers devoted to the derivation of the KdV or KdV-Burgers equation for arterial blood flows; see, for instance, Johnson (1971), Hashizume (1985), Cowley (1983), Yomosa (1987), Demiray (1996), Erbay et al (1992), Demiray (1997), Demiray and Dost (1998), Antar and Demiray (1999) and the references therein. Various approximations have been adopted; some are ad hoc and some can be justified as being asymptotically self-consistent.…”

Section: Introductionmentioning

confidence: 99%

Solitary waves in fluid-filled elastic tubes: existence, persistence, and the role of axial displacement

Ильичев

2010

IMA Journal of Applied Mathematics

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We re-examine the problem of solitary wave propagation in a fluid-filled elastic membrane tube using a much simplified procedure. It is shown that there may exist four families of solitary waves with speeds close to those given by the linear dispersion relation, whether the fluid is initially stationary or not, and that it is not asymptotically consistent to neglect the axial displacement even in a long-wave approximation. It is also shown that the solitary wave solutions obtained by neglecting higher-order terms persist for the full system of equations in the sense that the full system has solutions of the solitary-wave type and each exact solution is uniformly approximated by the corresponding leading-order solution.

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“…(10) can be simplified. In fact, incompressibility means that h * dA * = hdA (11) or using Eqs. (3,4) and (6) …”

Section: Governing Equationsmentioning

confidence: 99%

“…Several studies have investigated the effects of the axial displacement and found an increase in the predicted wave amplitude of 20% when it was retained [9][10][11]. In fact, Malfliet and Ndayrinde [6] suggest in their study that neglecting axial displacements have no significant effects.…”

Section: Introductionmentioning

confidence: 99%

The validity of the long-wave approximation for solitary waves in fluid-filled elastic tubes

Johnston

Epstein

2010

Z. Angew. Math. Phys.

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Studies of solitary waves commonly apply the long-wave approximation, which unnecessarily rigidifies the behavior of the tube, but permits the problem to be solved using certain approximate numerical techniques. In this study, an approach was developed where approximating the contribution of the axial strain as a linear function of the radial strain reduced the system of exact governing differential equations to a single equation of a single dependent variable. The approximated solution was found to agree with the exact solution to within 3%. This approach would be useful for considering more complex problems where the exact solution technique may not be reasonably applied. (2000). Primary 74J35; Secondary 76Z05. Mathematics Subject Classification

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Weakly nonlinear waves in a prestressed thin elastic tube containing a viscous fluid

Cited by 22 publications

References 18 publications

Modulation of electron-acoustic waves in a plasma with kappa distribution

Modulation of electron-acoustic waves in a plasma with kappa distribution

Solitary waves in fluid-filled elastic tubes: existence, persistence, and the role of axial displacement

The validity of the long-wave approximation for solitary waves in fluid-filled elastic tubes

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