Singular Gordon potentials are defined to be distributions from the space W −1 2,unif (R) that are sufficiently fast approximated by periodic ones. We prove that Schrödinger operators with singular Gordon potentials have no point spectrum and show that a rich class of quasiperiodic distributions consists of singular Gordon potentials .

In this paper, an algorithm based on the Drazin generalized conjugate residual (DGMRES) algorithm is proposed for computing the group-inverse solution of singular linear equations with index one. Numerical experiments show that the resulting group-inverse solution is reasonably accurate and its computation time is significantly less than that of group-inverse solution obtained by the DGMRES alg...

where p > , φp(x) = |x|p–x for x =  and φp() = , c ∈ Cn(R,R) and c(t + T) ≡ c(t), f is a continuous function defined in R and periodic in t with f (t, ·) = f (t + T , ·) and f (t, ) = , g(t,x) = g(x) + g(t,x), where g : R × (, +∞) → R is an L-Carathéodory function, g(t, ·) = g(t + T , ·), g ∈ C((,∞);R) has a singularity at x = , e : R→ R is a continuous periodic function with ...

This paper concerns homoclinic solutions to periodic orbits in a fourth-order Hamiltonian system arising from a reduction of the classical water-wave problem in the presence of surface tension. These solutions correspond to travelling solitary waves which converge to non-decaying ripples at innnity. An analytical result of Amick and Toland, showing the existence of such homoclinic orbits to sma...

We present a new technique, based on a clever numerical minimization of certain Sobolev norms, for the numerical solution of partial differential equations. The new method is very high order even for complex geometries and variable coefficient problems. One surprising feature of the method is that we prefer to pose the problem in first-order form. The system does not have to be square as long a...

in chemical engineering, several processes are represented by singular boundary value problems. in general, classical numerical methods fail to produce good approximations for the singular boundary value problems. in this paper, chebyshev finite difference (chfd) method and dtm-pad´e method, which is a combination of differential transform method (dtm) and pad´e approximant, are applied for sol...

Our paper studies the optical solitons for Kundu–Eckhaus (KE) equation with quintic nonlinearity and Raman effect. By applying improved modified extended tanh-function method, many soliton solutions can be obtained such as bright solutions, dark singular solution. In addition, we obtain various types of namely, periodic exponential rational Jacobi elliptic Weierstrass doubly solutions. Moreover...