With the help of computer symbolic computation software e.g., Maple , abundant interaction solutions of sine-Gordon equation are obtained by means of a constructed Wronskian form expansion method. The method is based upon the forms and structures of Wronskian solutions of sine-Gordon equation, and the functions used in the Wronskian determinants do not satisfy linear partial differential equati...

We prove that the Maxwell-Klein-Gordon equations on R relative to the Coulomb gauge are locally well-posed for initial data in H for all ε > 0. This builds on previous work by Klainerman and Machedon [3] who proved the corresponding result for a model problem derived from the Maxwell-Klein-Gordon system by ignoring the elliptic features of the system, as well as cubic terms.

We consider positive, radial and exponentially decaying steady state solutions of the general reaction-diffusion and Klein-Gordon type equations and present an explicit construction of infinite-dimensional invariant manifolds in the vicinity of these solutions. The result is a precise stable manifold theorem for the reaction-diffusion equation and a precise center-stable manifold theorem for th...

We give the governing equations for multiple scalar fields in a flat Friedmann-Robertson-Walker (FRW) background spacetime on all scales, allowing for metric and field perturbations up to second order. We then derive the Klein-Gordon equation at second order in closed form in terms of gaugeinvariant perturbations of the fields in the uniform curvature gauge. We also give a simplified form of th...

A system of equations is derived which must be satisfied by multiparticle matrix elements of any local operator in field theories with soliton behaviour. Form factors of various operators of interest are calculated exactly by means of the known exact S-matrices in the sine-Gordon, massive Thirring, non-linear a-, and Gross-Neveu models. The finite sine-Gordon wave function renormalization const...

We study four distinct second-order nonlinear equations of Rabelo which describe pseudospherical surfaces. By transforming these equations to the constant-characteristic form we relate them to some well-studied integrable equations. Two of the Rabelo equations are found to be related to the sine-Gordon equation. The other two are transformed into a linear equation and the Liouville equation, an...

I show that the compound modified Korteweg-de Vries-Sine-Gordon equations describe pseudospherical surfaces, that is, these equations are the integrability conditions for the structural equations of such surfaces. I obtain the self-Bäcklund transformations for these equations by a geometrical method and apply the Bäcklund transformations to these solutions and generate new traveling wave soluti...

The total momentum of a thermodynamically closed system is unique, as is the total energy. Nevertheless, there is continuing confusion concerning the correct form of the momentum and the energy–momentum tensor for an electromagnetic field interacting with a linear dielectric medium. Here we investigate the energy and momentum in a closed system composed of a propagating electromagnetic field an...

A system of coupled Klein-Gordon equations is proposed as a model for one-dimensional nonlinear wave processes in two-component media (e.g., long longitudinal waves in elastic bi-layers, where nonlinearity comes only from the bonding material). We discuss general properties of the model (Lie group classification, conservation laws, invariant solutions) and special solutions exhibiting an energy...