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We present the discovery of a class of exact spatially localized as well asperiodic wave solutions within the framework of the modified Korteweg-de Vriesequation. This class comprises breather and interacting soliton solutions aswell as interacting periodic wave solutions. The functional forms of thesesolutions include a joint parameter which can take both positive and negativevalues of unity. It is found that the existence of those closed form solutionsdepend strongly on whether the cubic nonlinearity parameter should beconsidered positive or negative. The derived wave structures show interestingproperties that may find practical applications.

Breather and interacting soliton and periodic waves for modified KdV equation