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Research Project Lineer Olmayan Üçlü Schrödinger Denklemi İçin Yapı Koruyan Sayısal Yöntemler(2016) Ertuğ, Sevim; Aydın, AyhanA nonlinear implicit energy-conserving scheme and a linearly implicit mass-conserving scheme are constructed for the numerical solution of a three-coupled nonlinear Schrödinger equation. Both methods are second order. The numerical experiments verify the theoretical results that while the nonlinear implicit scheme preserves the energy, the linearly implicit method preserves the mass of the system. In addition, the schemes are quite accurate in the preservation of the other conserved quantities of the system. Elastic collision, creation of new vector soliton, and fusion of soliton are observed in the solitary wave evolution. The numerical methods are proven to be highly efficient and stable in the simulation of the periodic and solitary waves of the equation in long terms. Dispersive analysis of the equation and the numerical methoda is investigated.
