光学ソリトン解法,動的および微分 perturbed ゲルジコフ-イバノフ方程式に対する感度分析
Muhammad Shakeel1, Fehaid Salem Alshammari2, Hameed Gul Ahmadzai3
1School of Mathematics and Statistics, Central South University, Changsha, 410083, China.
Scientific reports
|August 22, 2025
まとめ
この研究では,アタンガナを用いた非線形パルツジコフ・イバノフ方程式の新しい光学ソリトン解を見つけました.
科学分野:
- 非線形光学
- 数学物理学
- 分数式微積分
背景:
- 非線形モデルは 光ファイバー,通信,センシングにおいて 極めて重要です
- ソリトンダイナミクスを理解することは 信号伝送の鍵です
- 微分派生は高度なモデリング機能を提供します.
研究 の 目的:
- 非線形である Perturbed Gerdjikov-Ivanov (PGI) 方程式をアタンガナの派生式で区別するソリトン解を構築する.
- 高度分散の存在下で光学ソリトン溶液を分析する.
- 光学システムにおけるこれらのソリューションの応用を探求する.
主な方法:
- 微分 PGI 方程式を非線形普通微分方程式 (ODE) に変換する波形変換の適用
- サーダール次方程式 (SSE) 方法と一般化された統一方法を使用して,結果の ODE を解く.
- 得られた溶液のダイナミックと感度分析を行う.
主要な成果:
- 明るいソリトン,キックソリトン,周期性ソリトン,正確なダークソリトンなど,様々なソリトン溶液を成功裏に導出しました.
- 達成された解の振る舞いを視覚化するために,3D,2Dとコントールのグラフを提示します.
- ソリトンの特徴の形成における高次分散の重要性を示した.
結論:
- この研究では,分数 PGI 方程式のための多様なソリトン解を成功裏に構築し,分析しました.
- この発見は,光学系における非線形現象の理解に寄与する.
- 採用された方法は,類似の非線形モデルを分析するための堅固な枠組みを提供します.
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