Determining static stresses of deformed solitons

An equation for the quasi-static soliton ansatz depending on an arbitrary set of collective variables is covariantly derived on the basis of the variational approach to the method of collective variables. The field configuration and the static stresses of the deformed $\Phi^4$ kink that are produced by the excitation of the internal soliton mode are exactly determined. The kink interaction potential at large distances is considered for the example of the nonlinear Klein–Gordon system. A general approach to the problem of exactly determining the intersoliton potential for the entire set of physically admissible two-soliton configurations is discussed. The role of the gauge invariance of the resulting equations is elucidated in relation to the ambiguity in determining the intersoliton distance at the stage where the solitons lose their individuality as they approach each other.