In this paper, two solitary wave solutions are obtained for the Coupled Klein-Gordon-Schrodinger and Coupled quadratic nonlinear equations by the ansatz method. Both topological and non-topological solitary wave solutions are obtained.

A succinct presentation of the algebraic structure of the quantized Klein-Gordon field can be given in terms of a Lorentz invariant inner product. A presentation of a classical Klein-Gordon random field at non-zero temperature can be given in the same noncommutative algebraic style, allowing a detailed comparison of the quantized Klein-Gordon field with a classical Klein-Gordon random field.

The strong instability of ground state standing wave solutions eφω(x) for nonlinear Klein-Gordon equations has been known only for the case ω = 0. In this paper we prove the strong instability for small frequency ω.

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.

By exploiting estimates on Bloch functions obtained in a previous paper, we prove decay estimates for Klein Gordon equations with a time independent potential periodic in space in 1D and with generic mass. §

We prove the global well-posedness and we study the linear response for a system of two coupled equations composed of a Dirac equation for an infinite rank operator and a nonlinear wave or Klein-Gordon equation.

The stability of topological solitary waves and pulses in one-dimensional nonlinear Klein-Gordon systems is revisited. linearized equation describing small deviations around the static solution leads to a Sturm-Liouville problem, which solved systematic way for $-l\,(l+1)\,\sech^2(x)$-potential, showing orthogonality completeness relations fulfilled by set its solutions all values $l\in\mathbb{...