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<p>This paper studies a generalized heavenly equation, which includes the standard heavenly equation as a special case. The work starts from a vector nonlinear Riemann-Hilbert problem on the real axis. Next, the large-time asymptotic behavior for the solutions of the Cauchy problem is derived by solving the corresponding inverse Riemann-Hilbert problem. Then, by parameterizing the Riemann-Hilbert data, a class of implicit solutions is constructed.</p>

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A New Generalized Heavenly Equation and the Large-Time Behavior of its Solutions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月11日

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  • Yanmei Sun,
  • Zixiaoyi Ren

摘要

This paper studies a generalized heavenly equation, which includes the standard heavenly equation as a special case. The work starts from a vector nonlinear Riemann-Hilbert problem on the real axis. Next, the large-time asymptotic behavior for the solutions of the Cauchy problem is derived by solving the corresponding inverse Riemann-Hilbert problem. Then, by parameterizing the Riemann-Hilbert data, a class of implicit solutions is constructed.