Analytical Methods for Nonlinear Evolution Equations in Mathematical Physics
In this article, we will apply some of the algebraic methods to find great moving solutions to some nonlinear physical and engineering questions, such as a nonlinear (1 + 1) Ito integral differential equation and (1 + 1) nonlinear Schrödinger equation. To analyze practical solutions to these problem...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-12-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/8/12/2211 |
| _version_ | 1797544822741925888 |
|---|---|
| author | Khaled A. Gepreel |
| author_facet | Khaled A. Gepreel |
| author_sort | Khaled A. Gepreel |
| collection | DOAJ |
| description | In this article, we will apply some of the algebraic methods to find great moving solutions to some nonlinear physical and engineering questions, such as a nonlinear (1 + 1) Ito integral differential equation and (1 + 1) nonlinear Schrödinger equation. To analyze practical solutions to these problems, we essentially use the generalized expansion approach. After various <inline-formula><math display="inline"><semantics><mi>W</mi></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mi>G</mi></semantics></math></inline-formula> options, we get several clear means of estimating the plentiful nonlinear physics solutions. We present a process like-direct expansion process-method of expansion. In the particular case of <inline-formula><math display="inline"><semantics><mrow><msup><mi>W</mi><mo>′</mo></msup><mo>=</mo><mi>λ</mi><mi>G</mi></mrow></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><mrow><msup><mi>G</mi><mo>′</mo></msup><mo>=</mo><mi>μ</mi><mi>W</mi></mrow></semantics></math></inline-formula> in which <inline-formula><math display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula> and μ are arbitrary constants, we use the expansion process to build some new exact solutions for nonlinear equations of growth if it fulfills the decoupled differential equations. |
| first_indexed | 2024-03-10T14:06:00Z |
| format | Article |
| id | doaj.art-879d727b7c8f4cf9b3e5a3fc649606e8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T14:06:00Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-879d727b7c8f4cf9b3e5a3fc649606e82023-11-21T00:38:43ZengMDPI AGMathematics2227-73902020-12-01812221110.3390/math8122211Analytical Methods for Nonlinear Evolution Equations in Mathematical PhysicsKhaled A. Gepreel0Mathematics Department, Faculty of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaIn this article, we will apply some of the algebraic methods to find great moving solutions to some nonlinear physical and engineering questions, such as a nonlinear (1 + 1) Ito integral differential equation and (1 + 1) nonlinear Schrödinger equation. To analyze practical solutions to these problems, we essentially use the generalized expansion approach. After various <inline-formula><math display="inline"><semantics><mi>W</mi></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mi>G</mi></semantics></math></inline-formula> options, we get several clear means of estimating the plentiful nonlinear physics solutions. We present a process like-direct expansion process-method of expansion. In the particular case of <inline-formula><math display="inline"><semantics><mrow><msup><mi>W</mi><mo>′</mo></msup><mo>=</mo><mi>λ</mi><mi>G</mi></mrow></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><mrow><msup><mi>G</mi><mo>′</mo></msup><mo>=</mo><mi>μ</mi><mi>W</mi></mrow></semantics></math></inline-formula> in which <inline-formula><math display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula> and μ are arbitrary constants, we use the expansion process to build some new exact solutions for nonlinear equations of growth if it fulfills the decoupled differential equations.https://www.mdpi.com/2227-7390/8/12/2211direct algebraic methodsnonlinear Ito integro-differential equationdispersive nonlinear schrodinger equationexact solutions |
| spellingShingle | Khaled A. Gepreel Analytical Methods for Nonlinear Evolution Equations in Mathematical Physics Mathematics direct algebraic methods nonlinear Ito integro-differential equation dispersive nonlinear schrodinger equation exact solutions |
| title | Analytical Methods for Nonlinear Evolution Equations in Mathematical Physics |
| title_full | Analytical Methods for Nonlinear Evolution Equations in Mathematical Physics |
| title_fullStr | Analytical Methods for Nonlinear Evolution Equations in Mathematical Physics |
| title_full_unstemmed | Analytical Methods for Nonlinear Evolution Equations in Mathematical Physics |
| title_short | Analytical Methods for Nonlinear Evolution Equations in Mathematical Physics |
| title_sort | analytical methods for nonlinear evolution equations in mathematical physics |
| topic | direct algebraic methods nonlinear Ito integro-differential equation dispersive nonlinear schrodinger equation exact solutions |
| url | https://www.mdpi.com/2227-7390/8/12/2211 |
| work_keys_str_mv | AT khaledagepreel analyticalmethodsfornonlinearevolutionequationsinmathematicalphysics |