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New two-component vector breather solution of the modified Benjamin–Bona–Mahony (MBBM) equation is considered. Using the generalized perturbation reduction method, the MBBM equation is reduced to the coupled nonlinear Schrödinger equations for auxiliary functions. Explicit analytical expressions for the profile and parameters of the vector breather oscillating with the sum and difference of the frequencies and wavenumbers are presented. The two-component vector breather and single-component scalar breather of the MBBM equation is compared.

Breather solutions of modified Benjamin–Bona–Mahony equation