具有竞争非线性性的DNLS方程的内在局部化模式:分叉
G L Alfimov1, P A Korchagin1, F K Abdullaev2
1Moscow Institute of Electronic Engineering, Zelenograd, Moscow 124498, Russia.
Chaos (Woodbury, N.Y.)
|November 24, 2025
概括
我们研究了离散的非线性施罗丁格方程中的非线性局部模式,与竞争的非线性. 我们在不同模型中发现了内在局部化模式的普遍分叉行为,揭示了两个关键的解决方案分支.
科学领域:
- 非线性动力学是一种非线性动力学.
- 凝聚物质物理学 凝聚物质物理学
- 数学物理 数学物理
背景情况:
- 离散的非线性施罗丁格方程 (DNLS) 模拟了各种物理系统中的复杂现象.
- 竞争的非线性引入了丰富的动态行为,包括内在局部化模式 (ILM).
- 了解ILM对于在斯-爱因斯坦冷凝物和其他波浪系统中的应用至关重要.
研究的目的:
- 分析DNLS方程中的内在局部化模式 (ILM) 与立方-五度,四度-立方和立方-四度非线性.
- 调查合 (α) 和非线性平衡 (γ) 参数对ILM行为的影响.
- 在不同竞争的非线性模型中识别ILM的普遍特征和分支.
主要方法:
- 使用数字连续技术,从反连续极限 (α=0) 开始.
- 分析的重点是α-依赖ILM分支及其分叉,因为参数γ是不同的.
- 对三个不同的DNLS模型进行了全面的分支分析.
主要成果:
- 在所有三个研究的DNLS模型中确定了ILM的共同分叉模式,直至特定的分叉值.
- 在特定的 γ 范围 (0;γ) 内的 ILM 发现了正好两个通用∞-分支 (连接离散和连续极限).
- 证明了这些∞-分支表现出一个普遍的序列的分叉为γ变化.
结论:
- 该研究揭示了DNLS方程中的内在局部化模式的普遍分叉特性,具有竞争的非线性.
- 证实了两个基本的∞分支的存在和行为,提供了从离散到连续制度的过渡的见解.
- 结果提供了对不同竞争的非线性模型中非线性局部模式的统一理解.
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