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<p>This study establishes the existence of at least one standing wave, along with the corresponding homoclinic solution, for a class of matrix <i>nonlinear Schrödinger</i> (NLS) equations (or NLS systems) that encompass both time-dependent and time-independent formulations. The main innovations of this paper are as follows: Firstly, the nonlinearities considered exhibit a tripartite structure comprising sub-linear, asymptotically linear, and super-linear growth components. Secondly, these nonlinear terms may assume sign-changing characteristics. Thirdly, the analytical framework developed herein extends to scenarios involving concave-convex nonlinearities.</p>

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Solutions for Matrix NLS Equations with Tripartite and Sign-Changing Nonlinearities

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • Miao Zhang,
  • Guanwei Chen

摘要

This study establishes the existence of at least one standing wave, along with the corresponding homoclinic solution, for a class of matrix nonlinear Schrödinger (NLS) equations (or NLS systems) that encompass both time-dependent and time-independent formulations. The main innovations of this paper are as follows: Firstly, the nonlinearities considered exhibit a tripartite structure comprising sub-linear, asymptotically linear, and super-linear growth components. Secondly, these nonlinear terms may assume sign-changing characteristics. Thirdly, the analytical framework developed herein extends to scenarios involving concave-convex nonlinearities.