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Register a new userA Study about Finding Exact Solutions for Zeldovich Equation with Time-Dependent Coefficients by Using the Tanh Function Method
دراسة حول إيجاد الحلول التامة لمعادلة زيلدوفيتش ذات الأمثال التابعة للزمن باستخدام طريقة دالة الظل الزائدي
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Tishreen University ورقة بحثية
Publication date
2018
fields
Mathematics
and research's language is
العربية
Authors
سامي انجرو( باحث )
Created by
Shamra Editor
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هَدُفَ هذا البحث إلى إيجاد حلول تامة صريحة ذات موجة منعزلة (soliton wave solutions)، لمعادلة زيلدوفيتش ذات الأمثال التابعة للزمن، باستخدام طريقة دالة الظل الزائدي بتحويل موجي لاخطي في الحالة العامة، و تبين النتائج التي حصلنا عليها أن الحلول التامة تتأثر بالطبيعة اللاخطية للموجة، كما يتبين أن هذه الطريقة فعالة و مناسبة لحل مثل هذا النوع من المعادلات التفاضلية الجزئية غير الخطية التي تعتبر نماذج لمسائل تطبيقية في الفيزياء و الكيمياء و النمو السكاني.
In this work, we have been found explicit exact soliton wave solutions for Zeldovich equation with time-dependent coefficients, by using the tanh function method with nonlinear wave transform, in general case. The results obtained shows that these exact solutions are affected the nonlinear nature of the wave variable, it is also shown that this method is effective and appropriate for solving this kind of nonlinear PDEs, which are models of many applied problems in physics, chemistry and population evolution.
References used
Yang Y, Tao Z-l, Austin Francis R. Solutions of the generalized KdV equation with time-dependent damping and dispersion. App Math Comput 2010;216:1029–35
Triki H, Wazwaz AM. On soliton solutions for the Fitzhugh–Nagumo equation with time-dependent coefficients. Applied Mathematical Modelling 37 (2013) 3821–3828
Triki H, Wazwaz AM. Traveling wave solutions for fifth-order KdV type equations with timedependent coefficients. Commun. Nonlinear Sci. Numer. Simul. 2014;19:404– 408
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