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This article concerns an approximate solution for the Benjamin-Bona-Mahony (BBM) equation with a bilinear control in slowly varying medium. By a sharp estimation of the error term, a suitable approximate solution for this equation is established. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the modified Camassa–Holm equation is Painlevé integrable. We also study the orbital stability problem of negative solitary waves for this integrable equation. It is shown that the negative solitary waves are stable for arbitrary wave speed of propagation. [ABSTRACT FROM AUTHOR]

This paper studies low-regularity solutions of the periodic Fornberg–Whitham equation with initial value. The existence and the uniqueness of solutions are proved. The results are illustrated by considering the periodic peakons of the periodic Fornberg–Whitham equation. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global well posedness and limit behavior of the solutions to the viscous Degasperis–Procesi equation. We prove the global existence and uniqueness of solution to the viscous Degasperis–Procesi equation for u0∈L2(R). The local well posedness for u0∈L2(R) has been proven based on the energy estimate. The strong and weak limit behaviors of solution to the viscous Degasperis–Procesi equation are obtained. [ABSTRACT FROM AUTHOR]