tuned liquid dampers (tld) are among passive control devices that have been used to suppress the vibration of structures in recent years. these structures must be adequately presentable as an equivalent single degree of freedom system with long fundamental period. the tld, located at the top floors of the structure, can dissipate the external input energy into the system through the sloshing ef...

We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial diierential equations. Using the introduced deenition of reduction of diierential equations we establish equivalence of the non-classical (conditional symmetry) and direct (Ansatz) approaches to reduction of partial differential equat...

We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial differential equations. Using the introduced definition of reduction of differential equations we establish equivalence of the non-classical (conditional symmetry) and direct (Ansatz) approaches to reduction of partial differential eq...

Homotopy Perturbation Method is an effective method to find a solution of a nonlinear differential equation, subjected to a set of boundary condition. In this method a nonlinear and complex differential equation is transformed to series of linear and nonlinear and almost simpler differential equations. These set of equations are then solved secularly. Finally a linear combination of the solutio...

In this paper, the improved  -expansion method is proposed to solve the Kundu–Eckhaus equation and Gerdjikov–Ivanov model. The applied method are analytical methods to obtaining the exact solutions of nonlinear equations. Here, the aforementioned methods are used for constructing the soliton, periodic, rational, singular and solitary wave solutions for solving some equations. We obtained furthe...