A CIRCULAR SECTOR VIBRATION SYSTEM IN A POROUS MEDIUM

A circular sector is commonly used in a linkage mechanism, and its frequency property plays an important role in optimization of the linkage mechanism. Fast insight into its vibration property with simple calculation is very meaningful in scientific research. This paper studies the vibration of the circular sector in a porous medium (e.g. water), and a fractal-fractional oscillator is established using the two-scale fractal derivative. He’s frequency formula and Ma’s modification are used to elucidate the circular sector’s periodic property in a porous medium, the results show that the fractal dimension of the porous medium plays an important role in vibration attenuation

Exact Solutions of Two Nonlinear Space-time Fractional Differential Equations by Application of Exp-function Method

In this paper, we discuss on the exact solutions of the nonlinear space-time fractional Burgerlike equation and also the nonlinear fractional fifth-order Sawada-Kotera equation with the expfunction method.We use the functional derivatives in the sense of Riemann-Jumarie derivative and fractional convenient variable transformation in this study. Further, we obtain some exact analytical solutions including hyperbolic function

On solving the nonlinear Biswas-Milovic equation with dual-power law nonlinearity using the extended tanh-function method

In this article, we apply the extended tanh-function method to find the exact traveling wave solutions of the nonlinear Biswas-Milovic equation (BME), which describes the propagation of solitons through optical fibers for trans-continental and trans-oceanic distances. This equation is a generalized version of the nonlinear Schrödinger equation with dual-power law nonlinearity. With the aid of computer algebraic system Maple, both constant and time-dependent coefficients of BME are discussed. Comparison between our new results and the well-known results is given. The given method in this article is straightforward, concise and can be applied to other nonlinear partial differential equations (PDEs) in mathematical physics

Stationary and 2+1 dimensional integrable reductions of AKNS hierarchy

Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2004Includes bibliographical references (leaves: 72-82)Text in English; Abstract: Turkish and Englishvi, 84, leavesThe main concepts of the soliton theory and infinite dimensional Hamiltonian Systems, including AKNS (Ablowitz, Kaup, Newell, Segur) integrable hierarchy of nonlinear evolution equations are introduced.By integro-differential recursion operator for this hierarchy, several reductions to KDV, MKdV, mixed KdV/MKdV and Reaction-Diffusion system are constructed.The stationary reduction of the fifth order KdV is related to finite-dimensional integrable system of Henon-Heiles type.Different integrable extensions of Henon-Heiles model are found with corresponding separation of variables in Hamilton-Jacobi theory.Using the second and the third members of AKNS hierarchy, new method to solve 2+1 dimensional Kadomtsev-Petviashvili(KP-II) equation is proposed.By the Hirota bilinear method, one and two soliton solutions of KP-II are constructed and the resonance character of their mutual interactions are studied.By our bilinear form we first time created new four virtual soliton resonance solution for KPII.Finally, relations of our two soliton solution with degenerate four soliton solution in canonical Hirota form of KPII are established

Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies

Combining algebro-geometric methods and factorization techniques for finite difference expressions we provide a complete and self-contained treatment of all real-valued quasi-periodic finite-gap solutions of both the Toda and Kac-van Moerbeke hierarchies. In order to obtain our principal new result, the algebro-geometric finite-gap solutions of the Kac-van Moerbeke hierarchy, we employ particular commutation methods in connection with Miura-type transformations which enable us to transfer whole classes of solutions (such as finite-gap solutions) from the Toda hierarchy to its modified counterpart, the Kac-van Moerbeke hierarchy, and vice versa.Comment: LaTeX, to appear in Memoirs of the Amer. Math. So