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Yayın An application of the modified reductive perturbation method to a generalized boussinesq equation(Walter De Gruyter GMBH, 2013-02) Demiray, HilmiIn this work, we apply "the modified reductive perturbation method" to the generalized Boussinesq equation and obtain various form of generalized KdV equations as the evolution equations. Seeking a localized travelling wave solutions for these evolution equations we determine the scale parameters g(1) and g(2), which corresponds to the correction terms in the wave speed, so as to remove the possible secularities that might occur. Depending on the sign and the values of certain parameters the resulting solutions are shown to be a solitary wave or a periodic solution. The suitability of the method is also shown by comparing the results with the exact travelling wave solution for the generalized Boussinesq equation.Yayın Weakly nonlinear waves in elastic tubes filled with a layered fluid(Freund Publishing House, 2002) Demiray, HilmiIn this work we studied the propagation of weakly nonlinear waves in a prestressed thin elastic tube filled with an incompressible layered fluid, where the outer layer is assumed to be inviscid whereas the cylindrical core is considered to be viscous. Using the reductive perturbation technique, the propagation of weakly nonlinear waves in the longwave approximation is studied. The governing equation is shown to be the Korteweg-de Vries-Burgers' equation. A travelling wave type of solution for this evolution equation is sought and it is shown that with increasing core radius parameter the formation of strong shock wave becomes inevitable.
