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Yayın Particle dynamics in the KdV approximation(Elsevier Science BV, 2012-12) Borluk, Handan; Kalisch, HenrikThe KdV equation arises in the framework of the Boussinesq scaling as a model equation for waves at the surface of an inviscid fluid. Encoded in the KdV model are relations that may be used to reconstruct the velocity field in the fluid below a given surface wave. In this paper, velocity fields associated to exact solutions of the KdV equation are found, and particle trajectories are computed numerically. The solutions treated here comprise the solitary wave, periodic traveling waves, and the two-soliton solutions. For solitary waves and periodic traveling waves, approximate particle paths are found in closed form.Yayın Stability of solitary waves for three-coupled long wave-short wave interaction equations(Oxford Univ Press, 2011-08) Borluk, Handan; Erbay, SaadetIn this paper, we consider a three-component system of 1D long wave-short wave interaction equations. The system has two-parameter family of solitary wave solutions. We prove orbital stability of the solitary wave solutions using variational methods.
