Soliton perturbation theory for matrix complex modified Korteweg–de Vries equation

In this paper, soliton perturbation theory is extended to an integrable matrix equation. The explicit forms of the eigenstates and eigenvalues related to the linearized differential operator are found and therefore the first correction to the one soliton solution is established. A good agreement between the numerical simulations and analytical results is found. •Using the AKNS procedure, we determine a matrix version of the complex modified KdV equation.•The problem of the nearly integrable equation is transformed to a linearized differential operator.•We solve the later problem by expanding the solution and the source terms in terms of the eigenfunctions of the linearized operator.•The numerical simulations confirm the analytical results.