جواب‌های دقیق و تقریبی برای یک فرم تعمیم یافته از معادله غیرخطی شرودینگر
محورهای موضوعی : آمار
1 - استادیار ریاضی کاربردی، گروه علوم پایه، دانشگاه صنعتی کرمانشاه، ایران
کلید واژه: Symbolic computations, Exact solutions, Generalized exponential rational function method, The nonlinear Schrödinger equation, PDEs,
چکیده مقاله :
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.
In this paper, we consider a generalized form of nonlinear Schrodinger with second-order spatiotemporal dispersion coefficients. The generalized exponential rational function method (GERFM) have been used to obtain some novel exact optical solutions. Also, a new iterative method is successfully examined to numerical solution of the equation. Several numerical simulations are provided to show the behavior of the exact solution, and reveal the efficiently of the numerical results. It is apparent that both employed methods are simple but quite efficient for the extraction of solutions of the problem. Moreover, they are applicable for solving other nonlinear problems arising in mathematics, physics and other branches of engineering. All computations and numerical simulations are carried out with Mathematica. In this paper, we consider a generalized form of nonlinear Schrodinger with second-order spatiotemporal dispersion coefficients. The generalized exponential rational function method (GERFM) have been used to obtain some novel exact optical solutions. Also, a new iterative method is successfully examined to numerical solution of the equation. Several numerical simulations are provided to show the behavior of the exact solution, and reveal the efficiently of the numerical results. It is apparent that both employed methods are simple but quite efficient for the extraction of solutions of the problem. Moreover, they are applicable for solving other nonlinear problems arising in mathematics, physics and other branches of engineering. All computations and numerical simulations are carried out with Mathematica.
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