Abstract
We develop a new approach to the Lagrangian description of the bubble wall dynamics in the nonlinear Klein-Gordon equation with a two-vacuum potential of general form having a small vacuum energy difference. The approach is based on an ordinary differential equation governing the motion of an arbitrary point of the wall in the second approximation in the vacuum energy difference and inverse bubble radius. The equation is model independent: the concrete shape of the potential affects the constants involved only. We give a detailed derivation of this equation and present the full scheme of our method. As examples, we find some wall solutions for the ${\ensuremath{\varphi}}^{3}\ensuremath{-}{\ensuremath{\varphi}}^{4}$ and ${\ensuremath{\varphi}}^{4}\ensuremath{-}{\ensuremath{\varphi}}^{6}$ potentials and compare them with solutions obtained by the direct numerical integration of the nonlinear Klein-Gordon equation.
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