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非線形分数チェン・リー・リウモデルの単数と単数解のベータ派生
Akhtar Hussain1, Tarek F Ibrahim2,3, Faizah D Alanazi4
1Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan. akhtarhussain21@sms.edu.pk.
Scientific reports
|September 1, 2025
まとめ
研究者は非線形チェン・リー・リュー (NCLL) モデルを使用して光ファイバー通信を調査した. 新しい方法は,多様な単体および単体ソリューションを生み出し,システム設計とデータ伝送の信頼性を向上させました.
科学分野:
- 光学とフォトニクス
- 非線形動力学
- 数学モデリング
背景:
- 非線形チェン・リー・リュー (NCLL) モデルは,光ファイバー通信システムにとって不可欠です.
- 信号の質とデータレートを影響するノイズ,分散,非線形性を考慮します.
- NCLLモデルは,光ファイバーシステムの設計を最適化するのに役立ちます.
研究 の 目的:
- ベータデリバティブでNCLLモデルのための単体および単体溶液を調査する.
- 新しい拡張ハイパーボリック関数 (NEHF) と一般化された指数関数 (NGERF) を適用する.
- 光ファイバー通信のための新しい閉式ソリューションを作成し,検証します.
主な方法:
- シンボリック計算ツール (Mathematica 11.3, Maple) を利用した.
- ハイパーボリック,三角形,多項式,指数関数の解を導き出すために,新しい拡張型ハイパーボリック関数 (NEHF) を採用した.
- ハイパーボリック,トライゴノメトリック,指数関数の解を導き出すために,一般化された指数関数 (NGERF) の方法を使用した.
主要な成果:
- 周期,キンク,複数のソリトン,単一プロファイルを含む様々な閉式光学ソリトンソリューションを導出しました.
- 混合単数,混合ハイパーボリック,複合ショックソリューションなどの多様なソリューションタイプを特定しました.
- NCLL方程式に代入することによって,新たに導かれた解の正確性を検証した.
結論:
- NEHFとNGERFの方法は,NCLL方程式を解くのに信頼性があり,効率的です.
- これらの方法論は,幅広い光学ソリトンソリューションを生成することができます.
- この発見は,光ファイバー通信システムの理解と最適化に寄与する.
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