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<p>In this paper we consider the existence of standing waves for a coupled system of <i>k</i> equations with Lotka–Volterra type interaction. We prove the existence of a standing wave solution with all nontrivial components satisfying a prescribed asymptotic profile. In particular, the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(k-1\)</EquationSource> </InlineEquation>-last components of such solution exhibits a concentrating behavior, while the first one keeps a quantum nature. We analyze first in detail the result with three equations since this is the first case in which the coupling has a role contrary to what happens when only two densities appear. We also discuss the existence of solutions of this form for systems with other kind of couplings making a comparison with Lotka–Volterra type systems.</p>

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Partially concentrating solutions for systems with Lotka–Volterra type interactions

  • 期刊论文

  • 发表日期：

    2026年2月10日

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  • Sabrina Caputo,
  • Giusi Vaira

摘要

In this paper we consider the existence of standing waves for a coupled system of k equations with Lotka–Volterra type interaction. We prove the existence of a standing wave solution with all nontrivial components satisfying a prescribed asymptotic profile. In particular, the \(k-1\) -last components of such solution exhibits a concentrating behavior, while the first one keeps a quantum nature. We analyze first in detail the result with three equations since this is the first case in which the coupling has a role contrary to what happens when only two densities appear. We also discuss the existence of solutions of this form for systems with other kind of couplings making a comparison with Lotka–Volterra type systems.