Nonlinear stability of breather solutions to the coupled modified Korteweg-de Vries equations

•The exact new breather-type soliton solutions, which is generalize of the breather solutions.•We get stability tests via computing the generalized Weinstein conditions for the cmKdV breather solutions.•According to the conservation laws, we get variational characterization of breather solutions.•Through the analysis of the spectral stability, we present nonlinear stability of breather solutions to the cmKdV equations. This paper is concerned with the coupled modified Korteweg-de Vries (cmKdV) equations. We derive infinite conservation laws through the Lax pair of the cmKdV equations. Through the analysis of the spectral stability with the conservation laws, we obtain the nonlinear stability of breather solutions to the cmKdV equations.