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<p>We study the traveling wave solutions of the Burgers–Huxley equation from a geometric point of view via the qualitative theory of ordinary differential equations. Using the Poincaré compactification, we study the global phase portraits of a family of polynomial ordinary differential equations in the plane related to the Burgers–Huxley equation. We obtain the traveling wave solutions and their asymptotic behaviors from the orbits that connect equilibrium points, taking into account the restrictions of the studied equation.</p>

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Traveling wave solutions of the Burgers–Huxley equations

  • 期刊论文

  • 发表日期：

    2026年1月6日

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  • Luis Fernando Mello,
  • Ronisio Moises Ribeiro

摘要

We study the traveling wave solutions of the Burgers–Huxley equation from a geometric point of view via the qualitative theory of ordinary differential equations. Using the Poincaré compactification, we study the global phase portraits of a family of polynomial ordinary differential equations in the plane related to the Burgers–Huxley equation. We obtain the traveling wave solutions and their asymptotic behaviors from the orbits that connect equilibrium points, taking into account the restrictions of the studied equation.