In a two-field BPS sine-Gordon model, static soliton solutions are numerically shown to exhibit very slow attraction or repulsion caused by numerical noise exciting extra zero modes.
The First-Order Euler-Lagrange equations and some of their uses
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abstract
In many nonlinear field theories, relevant solutions may be found by reducing the order of the original Euler-Lagrange equations, e.g., to first order equations (Bogomolnyi equations, self-duality equations, etc.). Here we generalise, further develop and apply one particular method for the order reduction of nonlinear field equations which, despite its systematic and versatile character, is not widely known.
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Further comments on BPS systems
In a two-field BPS sine-Gordon model, static soliton solutions are numerically shown to exhibit very slow attraction or repulsion caused by numerical noise exciting extra zero modes.