Normalized solutions of nonlinear Dirac equations on noncompact metric graphs with localized nonlinearities

2025/05/21 by Zhentao He, Chao Ji, He, Zhentao +1 · 1 citation
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #advanced mathematical theories #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2505.15100

Abstract

In this paper, we study the following nonlinear Dirac equations (NLDE) on noncompact metric graph G with localized nonlinearities D u - ωu= aχ_K|u|^p-2u, where D is the Dirac operator on G, u: G → ℂ², ω∈ ℝ, a > 0, χ_K is the characteristic function of the compact core K, and p>2. First, for 22, prove the existence of normalized solutions to (NLDE) when λ= -mc² is an eigenvalue of the operator D. In the Appendix, we study the influence of the parameters m, c > 0 on the existence of normalized solutions to (NLDE). To the best of our knowledge, this is the first study to investigate the normalized solutions to (NLDE) on metric graphs.

Citations

• Sign-changing prescribed mass solutions for L²-supercritical NLS on compact metric graphs
• Normalized solutions of L²-supercritical NLS equations on noncompact metric graphs
• Infinitely many normalized solutions of L²-supercritical NLS equations on noncompact metric graphs with localized nonlinearities
• Normalized solutions of L²-supercritical NLS equations on compact metric graphs
• Uniqueness and non-uniqueness of prescribed mass NLS ground states on\n metric graphs
• Local minimizers in absence of ground states for the critical NLS energy\n on metric graphs
• Existence of infinite stationary solutions of the L²-subcritical and critical NLSE on compact metric graphs
• Multiple positive bound states for the subcritical NLS equation on metric graphs
• Threshold phenomena and existence results for NLS ground states on graphs
• NLS ground states on graphs
• Constrained energy minimization and orbital stability for the NLS equation on a star graph
• Fast solitons on star graphs

Cited by

• Nonrelativistic limit of normalized solutions of nonlinear Dirac equations on noncompact metric graphs with localized nonlinearities

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• Nonrelativistic limit of normalized solutions of nonlinear Dirac equations on noncompact metric graphs with localized nonlinearities
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• Normalized solutions for a nonlinear Dirac equation
• Bound states of nonlinear Dirac equations on periodic quantum graphs