The present article reviews methods from spectral theory and algebraic geometry for finding explicit solutions of the Toda equation, namely for the N -soliton solution and quasi-periodic solutions. Along they way basic concepts like Lax pairs, associated hierarchies, and Bäcklund transformations for the Toda equation are introduced.

This paper focuses on a fractal Phi-4 equation with time-space derivatives, though its solitary solutions have been deeply studied, periodic solution was rarely revealed due to strong non-linearity. Now the condition is completely changed, He?s frequency formulation provides universal tool having deep insight into property of equation. The two-scale transform used convert approximately differen...

Novel shape- and structural-controlled superparamagnetic nanostructures composed of self-supported spherical and rod-like CoFe(2)O(4) colloidal nanocrystals have been prepared by thermolysis of a stoichiometric Co(2+)Fe(2)(3+)-oleate complex in organic solution with periodic injection of hexane for controlling the nucleation, assembly, and growth of the nuclei.

The main purpose of this paper is to establish the existence of a solution of the semilinear Schrödinger equation −∆u + V (x)u = f(u), in R where V is a 1-periodic functions with respect to x, 0 lies in a gap of the spectrum of −∆ + V , and f(s) behaves like ± exp(αs) when s → ±∞.

in this paper, newton harmonic balance method (nhbm) is applied to obtain the analytical solution for an electron beam injected into a plasma tube where the magnetic field is cylindrical and increases towards the axis in inverse proportion to the radius. periodic solution is analytically verified and consequently the relation between the natural frequency and the amplitude is obtained in an ana...

The initial-boundary value problem associated with the motion of a Bingham fluid is considered. The existence and uniqueness of strong solution is proved under a certain assumption on the data. It is also shown that the solution exists globally in time when the data are small and that the solution converges to a periodic solution if the external force is time-periodic 0. Introduction. The purpo...

We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the diffusion 6oefficients are large, this solution represents a stable, spatially homogeneous time-periodic solution of the PDE. We show that when the diffusion coefficients become small, the spatially homoge...

the nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. using the leray-schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.

About a three-dimensional autonomous continuous Lorenz-like system. Through the full analysis of equilibrium points, we can derive the parameter condition of Hopf bifurcation; Next we adopt a Washout filter controller designed independently to control the Hopf bifurcation of the system, and the effect of the controller’s parameters on the position of bifurcation point, the bifurcation type, and...

We investigate the interaction of a periodic solution and a one-soliton solution for the spin-polarized current in a uniaxial ferromagnetic nanowire. The amplitude and wave number of the periodic solution for the spin current give different contributions to the width, velocity, and amplitude of the soliton. Moreover, we found that the soliton can be trapped only in space with proper conditions....