A relativistic extension of our pseudo-shifted l–expansion technique is presented to solve for the eigenvalues of Dirac and Klein-Gordon equations. Once more we show the numerical usefulness of its results via comparison with available numerical integration data.

We investigate the kink solutions to the generalized nonlinear Klein-Gordon equation in the presence of inhomogeneous forces and nonlocal operators. We have found that the number of kink internal modes can depend on the asymptotic behavior of the kink solution for large values of |x| . A list of mechanisms that are capable to create new kink internal modes would contain some of the following it...

We develop an alternative approach to study the effect of the generic perturbation (in addition to explicitly considering the loss term) in the nonlinear Klein-Gordon equations. By a change of the variables that cancel the dissipation term we are able to write the Lagrangian density and then, calculate the Lagrangian as a function of collective variables. We use the Lagrangian formalism togethe...

We prove a long time existence result for semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds. This generalizes a preceding result concerning the case of spheres, obtained in an earlier paper by the authors. The proof relies on almost orthogonality properties of products of eigenfunctions of positive elliptic selfadjoint operators on a compact manifold and on the specifi...

We consider a three dimensional perturbed Schrödinger operator H = −∆ + V (x), and the associated wave operators, that are defined as the strong L-limits limt→±∞ ee0 . We prove the boundedness of W± as operators onto L, for all p ∈ [1,∞], provided the potential V is small in the Rollnik and Kato norms. We use this result to obtain sharp dispersive estimates for Schrödinger, wave and Klein-Gordo...

We present a perturbation theory of kink solutions of discrete Klein-Gordon chains. The un-perturbed solutions correspond to the kinks of the adjoint partial differential equation. The perturbation theory is based on a reformulation of the discrete chain problem into a partial differential equation with spatially modulated mass density. The first order corrections to the kink solutions are obta...

‎a full nesterov-todd (nt) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using euclidean jordan algebra‎. ‎two types of‎ ‎full nt-steps are used‎, ‎feasibility steps and centering steps‎. ‎the‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...

In this paper we obtain a global characterization of the dynamics of even solutions to the one-dimensional nonlinear Klein-Gordon (NLKG) equation on the line with focusing nonlinearity |u|u, p > 5, provided their energy exceeds that of the ground state only sightly. The method is the same as in the three-dimensional case [15], the major difference being in the construction of the center-stable ...

  In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...