Approximate Homotopy Direct Reduction Method: Infinite Series Reductions to Perturbed mKdV Equations

Approximate homotopy symmetry and infinite series solutions to the perturbed mKdV equation

Approximate Symmetry Reduction Approach: Infinite Series Reduction to the Perturbed Burgers Equations

Abstract: From the approximate symmetry point of view, the perturbed burgers equation is investigated. The symmetry of a system of the corresponding PDEs which approximates the perturbed burgers equation is constructed and the corresponding general approximates symmetry reduction is derived, which enables infinite series solutions and general formulae. Study shows that the similarity solutions ...

Homotopy analysis method and its application for singularly perturbed delay differential equations with layer behavior

در این مقاله یک روش تحلیلی بر پایه‌ی روش تحلیل هموتوپی برای حل معادله دیفرانسیل-تفاضلی اختشاشی منفرد ارائه شده است. معادلات مورد بررسی در این مقاله از نوع تاخیری است که دارای رفتار لایه مرزی نیز هستند. تفاوت روش تحلیل هموتوپی با روشهای تحلیلی دیگر فراهم کردن یک راه ساده برای کنترل ناحیه همگرایی سری جواب بدست آمده معادله با استفاده از پارامتر کمکی تعبیه شده در این روش است. در این مقاله صحت و درس...

Modified homotopy method to solve non-linear integral equations

In this article we decide to define a modified homotopy perturbation for solving non-linear integral equations. Almost, all of the papers that was presented to solve non-linear problems by the homotopy method, they used from two non-linear and linear operators. But we convert a non-linear problem to two suitable non-linear operators also we use from appropriate bases functions such as Legendre ...

New explicit and Soliton Wave Solutions of Some Nonlinear Partial Differential Equations with Infinite Series Method

To start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ODE. Then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. It is required to state that the infinite series method is a well-organized method for obtaining exact s...