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Yayın Complex travelling wave solutions to the KdV and Burgers equations(Elsevier Science Inc, 2005-03) Demiray, HilmiIn 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.Yayın The modified reductive perturbation method as applied to Boussinesq equation: strongly dispersive case(Elsevier Science Inc, 2005-05-05) Demiray, HilmiIn this work, we extended the application of "the modified reductive perturbation method" to Boussinesq equation for strongly dispersive case and tried to obtain the contribution of higher order terms in the perturbation expansion. It is shown that the first order term in the perturbation expansion is governed by the non-linear Schrodinger equation and the second order term is governed by the linearized Schrodinger equation with a non-homogeneous term. In the long-wave limit, a travelling wave type of solution to these equations is also given.
