For defocusing mKdV with step initial data q_r >= q_l >= 0, long-time solutions split into a left modulated plane wave, a central modulated elliptic wave, and a right plane wave.
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Long-time asymptotics of the defocusing mKdV equation with step initial data
For defocusing mKdV with step initial data q_r >= q_l >= 0, long-time solutions split into a left modulated plane wave, a central modulated elliptic wave, and a right plane wave.