جواب‌هاي دقيق و تقريبي براي يك فرم تعميم يافته از معادله غيرخطي شرودينگر

Exact and approximate solutions for a generalized form of the Schrödinger nonlinear equation

در اين مقاله، يك فرم تعميم يافته از معادله غيرخطي شرودينگر همراه با ضريب پراكندگي مكاني از مرتبه دوم بررسي خواهد شد. در تعيين جواب‌هاي دقيق جديد اين معادله از روش توابع نمايي كسري تعميم يافته و در تعيين جواب‌هاي تقريبي از يك تكنيك عددي استفاده شده است. شبيه سازي‌هاي عددي مختلف نيز به منظور نمايش رفتار جواب‌هاي دقيق و نيز تاييد دقت روش عددي ارائه شده است. به وضوح مي‌توان ديد كه اين روش‌ها، روش‌هايي ساده در عين حال كارآمد در تعيين جواب‌هاي اين معادله هستند. به علاوه آن‌ها را مي‌توان در حل بسياري مسائل غيرخطي در رياضي، فيزيك و ساير شاخه‌هاي مهندسي به كارگرفت. در انجام كليه محاسبات و شبيه‌سازي‌هاي عددي از نرم افزار متمتيكا 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.