of the periodic nonlinear Schrödinger equation, where u(x, t) is a complex valued function in the class of smooth period one functions. In this work, we explain in what sense the generic level set of the constants of motion for the periodic nonlinear Schrödinger equation is an infinite dimensional torus, why the solution of the Hamiltonian equation is almost periodic in time, and describe how n...

In this paper, we investigate analytically and numerically the modulational instability in a model of nonlinear physical systems like nonlinear periodic lattices. This model is described by the discrete complex cubic quintic Ginzburg-Landau equation with non-local quintic term. We produce characteristics of the modulational instability in the form of typical dependences of the instability growt...

Algorithms and underlying mathematics are presented for numerical computation with periodic functions via approximations to machine precision by trigonometric polynomials, including the solution of linear and nonlinear periodic ordinary differential equations. Differences from the nonperiodic Chebyshev case are highlighted.

In this paper we will consider the nonlinear impulsive delay host–macroparasite model with periodic coefficients. By means of the continuation theorem of coincidence degree, we establish a sufficient condition for the existence of a positive periodic solution M(t) with strictly positive components. Moreover, we establish a sufficient condition for the global attractivity of M(t) and some suffic...

In this work, we study the existence of periodic solutions for partial neutral functional differential equation. We assume that the linear part is not necessarily densely defined and satisfies the Hille-Yosida condition. In the nonhomogeneous linear case, we prove that the existence of a bounded solution on R+ implies the existence of a periodic solution. In nonlinear case, we use the concept o...

a modified f-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (nlpdes) is discussed. we use this method to construct many new solutions to the nonlinear whitham-broer-kaup system (1+1)-dimensional. the solutions obtained include jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

We consider a nonlinear Volterra integro-differential equation with periodic solution, a special case of which has been used in modeling hematopoiesis dynamics. Some analytical results concerning existence and uniqueness of a positive periodic solution are presented together with some numerical results based on the reformulation of the equation as a system of ODEs and also from its direct solut...

We use extended mapping method and auxiliary equation method for finding new periodic wave solutions of nonlinear evolution equations in mathematical physics, and we obtain some new periodic wave solution for the Boussinesq system and the coupled KdV equations. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear pa...