fa مدل‌سازی سالیتونی جواب‌های تحلیلی معادله غیرخطی شرودینگر با قانون دوگانه غیرخطی جبر alg مقاله مستقل Original Manuscript &nbsp; <div><div id="ftn1"></div></div> <span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">در این پژوهش سعی بر این است تا با استفاده از روش جدیداً مطرح شده مبتنی بر ساختار نرم افزاری میپل<a href="#_ftn1" name="_ftnref1" title="">^{<span dir="LTR">^{<span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;">[1]</span></span>}</span>}</a></span>، تحت عنوان روش اصلاح شدۀ خاترز<a href="#_ftn2" name="_ftnref2" title="">^{<span dir="LTR">^{<span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;">[2]</span></span>}</span>}</a></span> جواب‌هایی از انواع جواب‌های سالیتونی، نمایی، هایپربولیک و مثلثاتی برای یکی از معادلات شرودینگر تحت عنوان معادلۀ غیرخطی شرودینگر با قانون دوگانه غیرخطی مطرح شود. با توجه به طیف گسترده استفاده از معادلۀ شرودینگر در فیزیک و مهندسی حل این معادله با استفاده از روش مذکور که در برگیرندۀ تنوع زیادی از جواب‌ها است اهمیت زیادی دارد</span> <div>&nbsp; <hr align="left" size="1" width="33%" > <div id="ftn2" style="text-align: left;"><span style="font-family:times new roman,serif;"><span style="font-size:8.0pt;">1. MAPLE</span></span><br> <span style="vertical-align:baseline;"><span style="font-family:times new roman,serif;"><span style="font-size:8.0pt;"><span style="vertical-align:baseline;"><span style="font-size:8pt;">[2]</span></span></span></span></span><span style="font-family:times new roman,serif;"><span style="font-size:8.0pt;">. </span></span><span style="font-family:times new roman,serif;"><span style="font-size:8.0pt;">Modified </span></span><span style="font-family:times new roman,serif;"><span style="font-size:8.0pt;">Khaters method</span></span></div> </div> <strong>Introduction</strong><br> In this study, we use a newly proposed method based on the software structure of the maple, called the Khaters method, and will be introducing exponential, hyperbolic, and trigonometric solutions for one of the Schr&ouml;dinger equations, called the nonlinear Schr&ouml;dinger equation with the dual power law nonlinearity. Given the widespread use of the Schr&ouml;dinger equation in physics and engineering, solving this equation is very important with the above method, which includes a large variety of solutions. Schr&ouml;dinger&#39;s nonlinear equation is a partial differential equation that plays a significant role in modern physics. Since quantum mechanics is present in the most modern technologies, such as nuclear energy, computers made of semiconductor materials, lasers, and all quantum phenomena, all the empirical observations of the world around us are consistent with the results of these equations. And this is the Schr&ouml;dinger equation describing the system of atomic particle motion and instrumentation over time. Hence, because of the importance of the solutions of the Schr&ouml;dinger equation, which describes many phenomena in physics and engineering, solving this equation is a great necessity. In every phenomenon and process in nature, there are various parameters that are in accordance with the rules governing that phenomenon. The expression of this relation in mathematical language is a functional equation, and the functional equation is derived from a phenomenon in which the tracks of a function change relative to one or several independent variables are studied, called the differential equation. Due to the nature of the Schr&ouml;dinger&#39;s equation, which contains different nonlinear sentences, is of great use in modern sciences, including Quantum Fiery. We can say that the widest range of applications of equations is related to the Schr&ouml;dinger equation, especially in physics and modern chemistry and quantum electronics. Wherever there are tiny particles, the Schr&ouml;dinger equation solves the analysis of the most complex issues associated with them<a href="./files/site1/files/42/10Abstract.pdf">./files/site1/files/42/10Abstract.pdf</a>  معادله غیرخطی شرودینگر, نرم افزار میپل, جواب‌های تحلیلی, روش اصلاح شدۀ خاترز, سالیتون. Nonlinear Schrodinger equation, Maple package, Analytical solutions, Khaters method, Soliton. 259 270 http://mmr.khu.ac.ir/browse.php?a_code=A-10-604-1&slc_lang=fa&sid=1 Ahmad Neirameh احمد نیرمه a.neirameh@gmail.com 10031947532846002473 10031947532846002473 Yes Gonbad Kavous University دانشگاه گنبد کاووس، دانشکدۀ علوم پایه، گروه ریاضی Saeed Shokooh سعید شکوه sd.shokooh@gmail.com 10031947532846002474 10031947532846002474 No Gonbad Kavous University دانشگاه گنبد کاووس، دانشکدۀ علوم پایه، گروه ریاضی