Pashaev, OktayDuruk, SelinPashaev, Oktay04.02. Department of Mathematics04. Faculty of Science01. Izmir Institute of Technology2014-07-222014-07-222009https://hdl.handle.net/11147/4064Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2009Includes bibliographical references (leaves: 79-82)Text in English; Abstract: Turkish and Englishix, 85 leavesThe Long-Short Wave interaction equations with adding quantum potential term and the Davey-Stewartson equation with addition of both, the quantum potential and the Hamiltonian terms are studied. These equations are reduced to different cases according to the choice of the quantum potential strength. For over critical case reductions to the non-linear diffusion-antidiffusion systems are derived. By the Hirota Direct Method one dissipaton solution of the system is derived. Two and three dissipaton (soliton) solutions are constructed explicitly. For special choice of the parameters they show the resonance character of interaction by fusion and fission of solitons.eninfo:eu-repo/semantics/openAccessQC174.26.W28 D96 2009Solitons--Mathematical modelsWave-motion, Theory ofWave equationMaster Thesis