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The nonlinear Riemann–Hilbert problems for a new general Pavlov equation

Author

Listed:
  • Zhang, Hongyi
  • Zhang, Yufeng
  • Lu, Huanhuan

Abstract

Manakov and Santini had studied the formal solutions and utilized the Riemann–Hilbert (RH) dressing method to investigate longtime behavior of the solutions and asymptotical implicit solutions of Pavlov equation (Manakov and Santini, 2007) and heavenly equation (Manakov and Santini, 2006). In the paper, we introduce a new Lax pair to construct an integrable system, which can be reduced to the standard Pavlov equation. Therefore, we refer to it as a generalized Pavlov equation. By utilizing the inverse scattering transform (IST) technique, we successfully derive the general formal solutions for the general Pavlov equation. Additionally, through the construction of a new RH problem, we investigate the longtime behavior of the solutions to the general Pavlov equation. The results presented in this paper expand upon the results previously presented by Manakov and Santini in their work (Manakov and Santini, 2007).

Suggested Citation

  • Zhang, Hongyi & Zhang, Yufeng & Lu, Huanhuan, 2024. "The nonlinear Riemann–Hilbert problems for a new general Pavlov equation," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:chsofr:v:185:y:2024:i:c:s0960077924007410
    DOI: 10.1016/j.chaos.2024.115189
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