جواب‌های دقیق و تقریبی برای یک فرم تعمیم یافته از معادله غیرخطی شرودینگر

الموضوعات :

بهزاد قنبری ¹ (استادیار ریاضی کاربردی، گروه علوم پایه، دانشگاه صنعتی کرمانشاه، ایران)

تاريخ الإرسال : 08 السبت , شعبان, 1440 تاريخ التأكيد : 12 الثلاثاء , ذو الحجة, 1440 تاريخ الإصدار : 06 الإثنين , جمادى الأولى, 1442

الکلمات المفتاحية: Symbolic computations, Exact solutions, Generalized exponential rational function method, The nonlinear Schrödinger equation, PDEs,

ملخص المقالة :

در این مقاله، یک فرم تعمیم یافته از معادله غیرخطی شرودینگر همراه با ضریب پراکندگی مکانی از مرتبه دوم بررسی خواهد شد. در تعیین جواب‌های دقیق جدید این معادله از روش توابع نمایی کسری تعمیم یافته و در تعیین جواب‌های تقریبی از یک تکنیک عددی استفاده شده است. شبیه سازی‌های عددی مختلف نیز به منظور نمایش رفتار جواب‌های دقیق و نیز تایید دقت روش عددی ارائه شده است. به وضوح می‌توان دید که این روش‌ها، روش‌هایی ساده در عین حال کارآمد در تعیین جواب‌های این معادله هستند. به علاوه آن‌ها را می‌توان در حل بسیاری مسائل غیرخطی در ریاضی، فیزیک و سایر شاخه‌های مهندسی به کارگرفت. در انجام کلیه محاسبات و شبیه‌سازی‌های عددی از نرم افزار متمتیکا استفاده شده است.

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