Abstract
In this paper, we investigate an extended complex modified Korteweg–de Vries equation. On zero background, based on Darboux transformation, breather solutions, breather molecules, breather-soliton molecules and breather-positons for extended complex modified Korteweg–de Vries equation are obtained by module resonance, velocity resonance and degenerate Darboux transformation. On nonzero background, breather solutions and breather-positons for extended complex modified Korteweg–de Vries equation are generated through Darboux transformation and degenerate Darboux transformation, respectively.
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