Abstract
Two new methods are used in order to obtain arbitrary approximate dromions solutions of the weakly nonlinear Klein-Gordon equation in 3 + 1 dimensions with one or more external fields. Using the asymptotic perturbation (AP) method, based on Fourier expansion and spatio-temporal rescaling, it is found that the amplitude slow modulation of Fourier modes is described by an integrable system of nonlinear evolution equations. In the first method only an external field is employed and single dromions with arbitrary height, shape and motion can be obtained, on the contrary in the second method multiple dromion solutions with arbitrary motion can be found by selecting appropriately a linear combination of external fields. Other coherent solutions (solitons, lumps and ring solitons) with arbitrary motion can be obtained, if the external fields are appropriately chosen. The two methods for dromion control can be easily applied to other nonlinear evolution equations.
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