Analytical and semi-analytical solutions for Phi-four equation through three recent schemes
This manuscript investigates the analytical and semi-analytical solutions of nonlinear phi-four (PF) equation by applying the sech–tanh expansion method, modified Ψ′Ψ-expansion method and Adomian decomposition method. This equation is considered as a particular case of the well-known Klein–Fock–Gord...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2021-03-01
|
| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379721001297 |
| _version_ | 1818343963604549632 |
|---|---|
| author | Mostafa M.A. Khater A.A. Mousa M.A. El-Shorbagy Raghda A.M. Attia |
| author_facet | Mostafa M.A. Khater A.A. Mousa M.A. El-Shorbagy Raghda A.M. Attia |
| author_sort | Mostafa M.A. Khater |
| collection | DOAJ |
| description | This manuscript investigates the analytical and semi-analytical solutions of nonlinear phi-four (PF) equation by applying the sech–tanh expansion method, modified Ψ′Ψ-expansion method and Adomian decomposition method. This equation is considered as a particular case of the well-known Klein–Fock–Gordon (KFG) equation. The KFG equation is derived by Oskar Klein and Walter Gordon and relates to Schrödinger equation. Many quantum effects can be studied based on the PF model’s solutions, such as wave-particle duality to describe reality in the form of waves is at the heart of quantum mechanics. The considered model is also used to explain de Broglie waves’ character, the spineless relativistic composite particles, relativistic electrons, etc., which are also the main icons for a good understanding of the phenomenon of quantum physics. Through two recent analytical schemes, handling this model gives many novel computational solutions that are tested through the semi-analytical scheme to investigate their accuracy. Demonstrating the obtained analytical and matching between analytical and semi-analytical through some distinct sketches shows the considered model’s novel physical properties. |
| first_indexed | 2024-12-13T16:38:56Z |
| format | Article |
| id | doaj.art-eb4ffb860a904657bc85c6efa645834d |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-13T16:38:56Z |
| publishDate | 2021-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-eb4ffb860a904657bc85c6efa645834d2022-12-21T23:38:20ZengElsevierResults in Physics2211-37972021-03-0122103954Analytical and semi-analytical solutions for Phi-four equation through three recent schemesMostafa M.A. Khater0A.A. Mousa1M.A. El-Shorbagy2Raghda A.M. Attia3Department of Mathematics, Faculty of Science, Jiangsu University, 212013 Zhenjiang, China; Department of Mathematics, Obour High Institute For Engineering and Technology, 11828 Cairo, Egypt; Corresponding author at:Department of Mathematics, Faculty of Science, Jiangsu University, 212013 Zhenjiang, China.Mathematics Department, Faculty of Science, Taif University, P.O.Box 11099, Taif 21944, Saudi ArabiaDepartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaDepartment of Basic Science, Higher Technological Institute, 44634 10th of Ramadan City, EgyptThis manuscript investigates the analytical and semi-analytical solutions of nonlinear phi-four (PF) equation by applying the sech–tanh expansion method, modified Ψ′Ψ-expansion method and Adomian decomposition method. This equation is considered as a particular case of the well-known Klein–Fock–Gordon (KFG) equation. The KFG equation is derived by Oskar Klein and Walter Gordon and relates to Schrödinger equation. Many quantum effects can be studied based on the PF model’s solutions, such as wave-particle duality to describe reality in the form of waves is at the heart of quantum mechanics. The considered model is also used to explain de Broglie waves’ character, the spineless relativistic composite particles, relativistic electrons, etc., which are also the main icons for a good understanding of the phenomenon of quantum physics. Through two recent analytical schemes, handling this model gives many novel computational solutions that are tested through the semi-analytical scheme to investigate their accuracy. Demonstrating the obtained analytical and matching between analytical and semi-analytical through some distinct sketches shows the considered model’s novel physical properties.http://www.sciencedirect.com/science/article/pii/S221137972100129701-0834A2537C50 |
| spellingShingle | Mostafa M.A. Khater A.A. Mousa M.A. El-Shorbagy Raghda A.M. Attia Analytical and semi-analytical solutions for Phi-four equation through three recent schemes Results in Physics 01-08 34A25 37C50 |
| title | Analytical and semi-analytical solutions for Phi-four equation through three recent schemes |
| title_full | Analytical and semi-analytical solutions for Phi-four equation through three recent schemes |
| title_fullStr | Analytical and semi-analytical solutions for Phi-four equation through three recent schemes |
| title_full_unstemmed | Analytical and semi-analytical solutions for Phi-four equation through three recent schemes |
| title_short | Analytical and semi-analytical solutions for Phi-four equation through three recent schemes |
| title_sort | analytical and semi analytical solutions for phi four equation through three recent schemes |
| topic | 01-08 34A25 37C50 |
| url | http://www.sciencedirect.com/science/article/pii/S2211379721001297 |
| work_keys_str_mv | AT mostafamakhater analyticalandsemianalyticalsolutionsforphifourequationthroughthreerecentschemes AT aamousa analyticalandsemianalyticalsolutionsforphifourequationthroughthreerecentschemes AT maelshorbagy analyticalandsemianalyticalsolutionsforphifourequationthroughthreerecentschemes AT raghdaamattia analyticalandsemianalyticalsolutionsforphifourequationthroughthreerecentschemes |