New Exact Solutions of the Conformable Space-Time Sharma–Tasso–Olver Equation Using Two Reliable Methods
The major purpose of this article is to seek for exact traveling wave solutions of the nonlinear space-time Sharma–Tasso–Olver equation in the sense of conformable derivatives. The novel <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/4/644 |
| _version_ | 1797570300448079872 |
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| author | Sekson Sirisubtawee Sanoe Koonprasert Surattana Sungnul |
| author_facet | Sekson Sirisubtawee Sanoe Koonprasert Surattana Sungnul |
| author_sort | Sekson Sirisubtawee |
| collection | DOAJ |
| description | The major purpose of this article is to seek for exact traveling wave solutions of the nonlinear space-time Sharma–Tasso–Olver equation in the sense of conformable derivatives. The novel <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mfrac> <msup> <mi>G</mi> <mo>′</mo> </msup> <mi>G</mi> </mfrac> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-expansion method and the generalized Kudryashov method, which are analytical, powerful, and reliable methods, are used to solve the equation via a fractional complex transformation. The exact solutions of the equation, obtained using the novel <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mfrac> <msup> <mi>G</mi> <mo>′</mo> </msup> <mi>G</mi> </mfrac> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-expansion method, can be classified in terms of hyperbolic, trigonometric, and rational function solutions. Applying the generalized Kudryashov method to the equation, we obtain explicit exact solutions expressed as fractional solutions of the exponential functions. The exact solutions obtained using the two methods represent some physical behaviors such as a singularly periodic traveling wave solution and a singular multiple-soliton solution. Some selected solutions of the equation are graphically portrayed including 3-D, 2-D, and contour plots. As a result, some innovative exact solutions of the equation are produced via the methods, and they are not the same as the ones obtained using other techniques utilized previously. |
| first_indexed | 2024-03-10T20:24:00Z |
| format | Article |
| id | doaj.art-3449f69f1bf945cfa2ffb814cfb8dc7b |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T20:24:00Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-3449f69f1bf945cfa2ffb814cfb8dc7b2023-11-19T21:56:29ZengMDPI AGSymmetry2073-89942020-04-0112464410.3390/sym12040644New Exact Solutions of the Conformable Space-Time Sharma–Tasso–Olver Equation Using Two Reliable MethodsSekson Sirisubtawee0Sanoe Koonprasert1Surattana Sungnul2Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandDepartment of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandDepartment of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandThe major purpose of this article is to seek for exact traveling wave solutions of the nonlinear space-time Sharma–Tasso–Olver equation in the sense of conformable derivatives. The novel <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mfrac> <msup> <mi>G</mi> <mo>′</mo> </msup> <mi>G</mi> </mfrac> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-expansion method and the generalized Kudryashov method, which are analytical, powerful, and reliable methods, are used to solve the equation via a fractional complex transformation. The exact solutions of the equation, obtained using the novel <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mfrac> <msup> <mi>G</mi> <mo>′</mo> </msup> <mi>G</mi> </mfrac> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-expansion method, can be classified in terms of hyperbolic, trigonometric, and rational function solutions. Applying the generalized Kudryashov method to the equation, we obtain explicit exact solutions expressed as fractional solutions of the exponential functions. The exact solutions obtained using the two methods represent some physical behaviors such as a singularly periodic traveling wave solution and a singular multiple-soliton solution. Some selected solutions of the equation are graphically portrayed including 3-D, 2-D, and contour plots. As a result, some innovative exact solutions of the equation are produced via the methods, and they are not the same as the ones obtained using other techniques utilized previously.https://www.mdpi.com/2073-8994/12/4/644nonlinear conformable space-time Sharma–Tasso–Olver equationconformable derivativenovel (<named-content content-type="inline-formula"> <mml:math id="mm500" display="block"> <mml:semantics> <mml:mrow> <mml:mfrac> <mml:msup> <mml:mi>G</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mi>G</mml:mi> </mml:mfrac> </mml:mrow> </mml:semantics> </mml:math> </named-content>)-expansion methodgeneralized Kudryashov methodsingular kink-type solutionsingular multiple-soliton solution |
| spellingShingle | Sekson Sirisubtawee Sanoe Koonprasert Surattana Sungnul New Exact Solutions of the Conformable Space-Time Sharma–Tasso–Olver Equation Using Two Reliable Methods Symmetry nonlinear conformable space-time Sharma–Tasso–Olver equation conformable derivative novel (<named-content content-type="inline-formula"> <mml:math id="mm500" display="block"> <mml:semantics> <mml:mrow> <mml:mfrac> <mml:msup> <mml:mi>G</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mi>G</mml:mi> </mml:mfrac> </mml:mrow> </mml:semantics> </mml:math> </named-content>)-expansion method generalized Kudryashov method singular kink-type solution singular multiple-soliton solution |
| title | New Exact Solutions of the Conformable Space-Time Sharma–Tasso–Olver Equation Using Two Reliable Methods |
| title_full | New Exact Solutions of the Conformable Space-Time Sharma–Tasso–Olver Equation Using Two Reliable Methods |
| title_fullStr | New Exact Solutions of the Conformable Space-Time Sharma–Tasso–Olver Equation Using Two Reliable Methods |
| title_full_unstemmed | New Exact Solutions of the Conformable Space-Time Sharma–Tasso–Olver Equation Using Two Reliable Methods |
| title_short | New Exact Solutions of the Conformable Space-Time Sharma–Tasso–Olver Equation Using Two Reliable Methods |
| title_sort | new exact solutions of the conformable space time sharma tasso olver equation using two reliable methods |
| topic | nonlinear conformable space-time Sharma–Tasso–Olver equation conformable derivative novel (<named-content content-type="inline-formula"> <mml:math id="mm500" display="block"> <mml:semantics> <mml:mrow> <mml:mfrac> <mml:msup> <mml:mi>G</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mi>G</mml:mi> </mml:mfrac> </mml:mrow> </mml:semantics> </mml:math> </named-content>)-expansion method generalized Kudryashov method singular kink-type solution singular multiple-soliton solution |
| url | https://www.mdpi.com/2073-8994/12/4/644 |
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