in this paper, a reliable approach is introduced to approximate periodic solutions of a system of coupled integrable dispersionless. the system is firstly, transformed into an ordinary differential equation by wave transformation. the solution of ode is obtained by the homotopy perturbation method. to show the periodic behavior of the solution, a modification based on the laplace transforms and...

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...

We consider the mapping properties of integral operator arising in nonlocal slender body theory (SBT) for model geometry a straight, periodic filament. It is well known that classical singular SBT suffers from high wavenumber instabilities, making it unsuitable approximating inverse problem, where fiber velocity prescribed and must be inverted to find force density along fiber. Regularizations ...

We analyze a family of singular Schrödinger operators describing a Neumann waveguide with a periodic array of singular traps of a δ′ type. We show that in the limit when perpendicular size of the guide tends to zero and the δ′ interactions are appropriately scaled, the first spectral gap is determined exclusively by geometric properties of the traps.

In this work we consider smooth orthonormal factorizations of smooth matrixvalued functions of constant rank. In particular, we look at Schur, singular value, and related decompositions. Furthermore, we consider the case in which the functions are periodic and study periodicity of the factors. We allow for eigenvalues and singular values to coalesce.