A direct approach to the model of few‐optical‐cycle solitons beyond the slowly varying envelope approximation

In this paper, we present a direct approach to various solutions of the modified Korteweg‐de Vries‐sine Gordon equation, which is a versatile model emerging in many physics and mathematics contexts. The direct approach is based on Cauchy matrix and Sylvester equation. The obtained solutions can be classified with respect to eigenvalues of certain matrix. We present eigenvalue structures that give rise to kinks, breathers, soliton molecules, multiple‐pole solutions, and so forth. Some obtained solutions are illustrated.

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