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2003 - 20053
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Yazar: Demiray, Hilmi × Konu: Functions ×

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    A travelling wave solution to the KdV-Burgers equation
    (Elsevier Inc, 2004-07-15) Demiray, Hilmi
    In the present work, by introducing a new potential function and by using the hyperbolic tangent method and an exponential rational function approach, a travelling wave solution to the KdV-Burgers (KdVB) equation is presented. It is observed that both methods lead to the same type of solution. The solution method we introduced here is less restrictive and comprises some solutions existing in the current literature [Wave Motion 11 (1989) 559; Wave Motion 14 (1991) 559].
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    Complex travelling wave solutions to the KdV and Burgers equations
    (Elsevier Science Inc, 2005-03) Demiray, Hilmi
    In the present work, making use of the hyperbolic tangent method, some complex travelling wave solutions to the Korteweg-deVries and Burgers equations are obtained. It is observed that the real part of the Solution for the Burgers equation is of shock type whereas the imaginary part is the localized travelling wave. However, for the solution of the Korteweg-deVries equation the real part is a solitary wave while the imaginary part is the product of a solitary wave with a shock.
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    Nonlinear wave modulation in a fluid-filled linearly tapered elastic tube
    (Gauthier-Villars/Editions Elsevier, 2003-08) Demiray, Hilmi
    In the present work, treating the arteries as a thin-walled, linearly tapered, prestressed elastic tube and using the reductive perturbation method, we have studied the amplitude modulation of nonlinear waves in such a fluid-filled elastic tube. By considering the blood as an incompressible viscous fluid, the evolution equation is obtained as the dissipative nonlinear Schrodinger equation with variable coefficient. It is shown that this type of evolution equations admit a solitary wave type of solution with variable wave speeds and amplitude. It is observed that, the speed of enveloping wave increases with the scaled time parameter tau for negative tapering angle while it decreases for positive tapering. On the other hand, the speed of harmonic wave increases for positive tapering whereas it decreases for negative tapering.