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Construction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH Equation

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  • Hao Yu
  • Aiyong Chen
  • Kelei Zhang

Abstract

For the generalized mCH equation, we construct a 2-peakon solution on both the line and the circle, and we can control the size of the initial data. The two peaks at different speeds move in the same direction and eventually collide. This phenomenon is that the solution at the collision time is consistent with another solitary peakon solution. By reversing the time, we get two new solutions with the same initial value and different values at the rest of the time, which means the nonuniqueness for the equation in Sobolev spaces is proved for .

Suggested Citation

  • Hao Yu & Aiyong Chen & Kelei Zhang, 2021. "Construction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH Equation," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-10, November.
    • Handle: RePEc:hin:jnlamp:9363673
    DOI: 10.1155/2021/9363673
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