| Abstract: |
| In this talk, we report the long-time asymptotic behavior for the Cauchy problem of the modified Camassa-Holm (mCH) equation with finite density initial data in different regions. We prove that the soliton resolution conjecture holds, that is, the solution of the mCH equation can be expressed as the soliton solution on the discrete spectrum, the leading term on the continuous spectrum, and the residual error. This work is joint with Jin-JIe Yang and Zhi-Qiang Li. |
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