Harmonic Analysis Method for Nonlinear Evolution Equations, I

10.1142/8209 ◽  
2011 ◽  
Author(s):  
Baoxiang Wang ◽  
Zhaohui Huo ◽  
Chengchun Hao ◽  
Zihua Guo
Keyword(s):  
Harmonic Analysis ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Analysis Method ◽  
Harmonic Analysis Method

scholarly journals Application of the homotopy analysis method to solving nonlinear evolution equations

2006 ◽  
Vol 55 (4) ◽  
pp. 1555
Author(s):  
Shi Yu-Ren ◽  
Xu Xin-Jian ◽  
Wu Zhi-Xi ◽  
Wang Ying-Hai ◽  
Yang Hong-Juan ◽  
...  
Keyword(s):  
Homotopy Analysis Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Analysis Method ◽  
Homotopy Analysis

New Applications of the Homotopy Analysis Method

2008 ◽  
Vol 63 (7-8) ◽  
pp. 385-392 ◽  
Author(s):  
Elsayed Abd Elaty Elwakil ◽  
Mohamed Aly Abdou
Keyword(s):  
Exact Solutions ◽  
Homotopy Analysis Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Problems ◽  
Nonlinear Evolution Equations ◽  
Analysis Method ◽  
Validity And Reliability ◽  
Analytical Technique ◽  
Homotopy Analysis

An analytical technique, namely the homotopy analysis method (HAM), is applied using a computerized symbolic computation to find the approximate and exact solutions of nonlinear evolution equations arising in mathematical physics. The HAM is a strong and easy to use analytic tool for nonlinear problems and does not need small parameters in the equations. The validity and reliability of the method is tested by application on three nonlinear problems, namely theWhitham-Broer-Kaup equations, coupled Korteweg-de Vries equation and coupled Burger’s equations. Comparisons are made between the results of the HAM with the exact solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

scholarly journals The unified method for abundant soliton solutions of local time fractional nonlinear evolution equations

2021 ◽  
Vol 22 ◽  
pp. 103979
Author(s):  
Nauman Raza ◽  
Muhammad Hamza Rafiq ◽  
Melike Kaplan ◽  
Sunil Kumar ◽  
Yu-Ming Chu
Keyword(s):  
Local Time ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
The Unified Method ◽  
Unified Method
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