  We show that wave breaking occurs for the modified Camassa-Holm (mCH)
equation. Next we classify all traveling wave solutions of the modified
Camassa-Holm equation in the weak sense via parametrization of their maxima,
minima and wave velocity constants. This equation is shown to admit in addition
to more popular solutions like smooth traveling waves and peakons, some not so
well-known traveling waves as, for example, kinks, cuspons, composite waves and
stumpons. Moreover, explicit peakons in terms of Jacobian elliptic functions
are found.
