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<p>In this paper, we study meromorphic solutions of a class of nonlinear partial differential equations with the help of Nevanlinna theory of meromorphic mappings from a parabolic complex manifold into <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_779_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {P}}^{n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>. This class of partial differential equations is related to some mKdv equations, gKdv equations, Burgers’ equations, Allen–Cahn equations.</p>

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Meromorphic solutions of a class of nonlinear partial differential equations

  • 期刊论文

  • 发表日期：

    2025年3月29日

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  • Wenjie Hao,
  • Qingcai Zhang

摘要

In this paper, we study meromorphic solutions of a class of nonlinear partial differential equations with the help of Nevanlinna theory of meromorphic mappings from a parabolic complex manifold into \({\mathbb {P}}^{n}\) P n . This class of partial differential equations is related to some mKdv equations, gKdv equations, Burgers’ equations, Allen–Cahn equations.