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March 14, 2026Journal of Nonlinear Mathematical Physics0 citationsOpen Access

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

YSYanmei SunZRZixiaoyi Ren

Key Points

  • To investigate the large-time behavior of solutions for a generalized heavenly equation derived from a Riemann-Hilbert problem.
  • Developed a vector nonlinear Riemann-Hilbert problem on the real axis.
  • Derived large-time asymptotic behavior for solutions of the Cauchy problem.
  • Solved the corresponding inverse Riemann-Hilbert problem for analysis.
  • Constructed implicit solutions by parameterizing Riemann-Hilbert data.
  • Successfully derived asymptotic behaviors for the generalized heavenly equation solutions.
  • Identified connections to standard heavenly equation solutions as special cases.
  • Presented a new class of implicit solutions based on parameterization of data.

Abstract

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.

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Cite This Study

Sun et al. (2026) studied this question.

synapsesocial.com/papers/69b4fc1fb39f7826a300cd6dhttps://doi.org/10.1007/s44198-026-00403-y
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