Wave propagation in N-species Lotka-Volterra competition systems with diffusion

Cheng Hsiung Hsu, Jian Jhong Lin

Research output: Contribution to journalArticlepeer-review


This paper is concerned with the propagation of traveling wave solutions for diffusive N-species Lotka-Volterra competition systems. We first establish an innovative lemma relating to the existence of positive solutions for the transpose systems of linear systems. Then a necessary and sufficient condition is established for the existence of non-decreasing traveling wave solutions connecting two different equilibria. In addition, using the two-sided Laplace transform, we can obtain the asymptotic behavior of traveling wave solutions at positive infinity. Based on the properties of asymptotic behavior, we show that all non-critical traveling wave solutions with the same wave speed are unique up to translations. We also provide an example to support our result.

Original languageEnglish
Article number127255
JournalJournal of Mathematical Analysis and Applications
Issue number2
StatePublished - 15 Oct 2023


  • Asymptotic behavior
  • Lotka-Volterra competition systems
  • Sub-solution and super-solution
  • Traveling wave solutions
  • Two-sided Laplace transform
  • Uniqueness


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