Complex mixed dark-bright wave patterns to the modified α and modified Vakhnenko-Parkes equations

In this paper, we present the sine-Gordon expansion method to prepare the mixed dark bright wave patterns to the nonlinear partial differential equations arising in mathematical physics. Then, we apply the proposed method for a credible recourse of two nonlinear physical models: the modified Vakhnen...
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Autor*in:	Haci Mehmet Baskonus [verfasserIn] Juan Luis García Guirao [verfasserIn] Ajay Kumar [verfasserIn] Fernando S. Vidal Causanilles [verfasserIn] German Rodriguez Bermudez [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	35Axx 35Lxx 35Qxx

Übergeordnetes Werk:	In: Alexandria Engineering Journal - Elsevier, 2016, 59(2020), 4, Seite 2149-2160
Übergeordnetes Werk:	volume:59 ; year:2020 ; number:4 ; pages:2149-2160

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1016/j.aej.2020.01.032

Katalog-ID:	DOAJ001753509

Internformat


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publishDate	2020
allfields	10.1016/j.aej.2020.01.032 doi (DE-627)DOAJ001753509 (DE-599)DOAJ4558f2f028fa475fb50028bca63872a4 DE-627 ger DE-627 rakwb eng TA1-2040 Haci Mehmet Baskonus verfasserin aut Complex mixed dark-bright wave patterns to the modified α and modified Vakhnenko-Parkes equations 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we present the sine-Gordon expansion method to prepare the mixed dark bright wave patterns to the nonlinear partial differential equations arising in mathematical physics. Then, we apply the proposed method for a credible recourse of two nonlinear physical models: the modified Vakhnenko-Parkes and modified α-equation. These exact solutions comprise the hyperbolic, trigonometric, rational and exponential function with few licentious parameter. The analytical solutions have different physical structures and they are graphically analyzed in order to show their dynamical behavior by means of 2D, 3D and contour plots. 35Axx 35Lxx 35Qxx Engineering (General). Civil engineering (General) Juan Luis García Guirao verfasserin aut Ajay Kumar verfasserin aut Fernando S. Vidal Causanilles verfasserin aut German Rodriguez Bermudez verfasserin aut In Alexandria Engineering Journal Elsevier, 2016 59(2020), 4, Seite 2149-2160 (DE-627)669887609 (DE-600)2631413-7 20902670 nnns volume:59 year:2020 number:4 pages:2149-2160 https://doi.org/10.1016/j.aej.2020.01.032 kostenfrei https://doaj.org/article/4558f2f028fa475fb50028bca63872a4 kostenfrei http://www.sciencedirect.com/science/article/pii/S1110016820300338 kostenfrei https://doaj.org/toc/1110-0168 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 59 2020 4 2149-2160
spelling	10.1016/j.aej.2020.01.032 doi (DE-627)DOAJ001753509 (DE-599)DOAJ4558f2f028fa475fb50028bca63872a4 DE-627 ger DE-627 rakwb eng TA1-2040 Haci Mehmet Baskonus verfasserin aut Complex mixed dark-bright wave patterns to the modified α and modified Vakhnenko-Parkes equations 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we present the sine-Gordon expansion method to prepare the mixed dark bright wave patterns to the nonlinear partial differential equations arising in mathematical physics. Then, we apply the proposed method for a credible recourse of two nonlinear physical models: the modified Vakhnenko-Parkes and modified α-equation. These exact solutions comprise the hyperbolic, trigonometric, rational and exponential function with few licentious parameter. The analytical solutions have different physical structures and they are graphically analyzed in order to show their dynamical behavior by means of 2D, 3D and contour plots. 35Axx 35Lxx 35Qxx Engineering (General). Civil engineering (General) Juan Luis García Guirao verfasserin aut Ajay Kumar verfasserin aut Fernando S. Vidal Causanilles verfasserin aut German Rodriguez Bermudez verfasserin aut In Alexandria Engineering Journal Elsevier, 2016 59(2020), 4, Seite 2149-2160 (DE-627)669887609 (DE-600)2631413-7 20902670 nnns volume:59 year:2020 number:4 pages:2149-2160 https://doi.org/10.1016/j.aej.2020.01.032 kostenfrei https://doaj.org/article/4558f2f028fa475fb50028bca63872a4 kostenfrei http://www.sciencedirect.com/science/article/pii/S1110016820300338 kostenfrei https://doaj.org/toc/1110-0168 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 59 2020 4 2149-2160
allfields_unstemmed	10.1016/j.aej.2020.01.032 doi (DE-627)DOAJ001753509 (DE-599)DOAJ4558f2f028fa475fb50028bca63872a4 DE-627 ger DE-627 rakwb eng TA1-2040 Haci Mehmet Baskonus verfasserin aut Complex mixed dark-bright wave patterns to the modified α and modified Vakhnenko-Parkes equations 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we present the sine-Gordon expansion method to prepare the mixed dark bright wave patterns to the nonlinear partial differential equations arising in mathematical physics. Then, we apply the proposed method for a credible recourse of two nonlinear physical models: the modified Vakhnenko-Parkes and modified α-equation. These exact solutions comprise the hyperbolic, trigonometric, rational and exponential function with few licentious parameter. The analytical solutions have different physical structures and they are graphically analyzed in order to show their dynamical behavior by means of 2D, 3D and contour plots. 35Axx 35Lxx 35Qxx Engineering (General). Civil engineering (General) Juan Luis García Guirao verfasserin aut Ajay Kumar verfasserin aut Fernando S. Vidal Causanilles verfasserin aut German Rodriguez Bermudez verfasserin aut In Alexandria Engineering Journal Elsevier, 2016 59(2020), 4, Seite 2149-2160 (DE-627)669887609 (DE-600)2631413-7 20902670 nnns volume:59 year:2020 number:4 pages:2149-2160 https://doi.org/10.1016/j.aej.2020.01.032 kostenfrei https://doaj.org/article/4558f2f028fa475fb50028bca63872a4 kostenfrei http://www.sciencedirect.com/science/article/pii/S1110016820300338 kostenfrei https://doaj.org/toc/1110-0168 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 59 2020 4 2149-2160
allfieldsGer	10.1016/j.aej.2020.01.032 doi (DE-627)DOAJ001753509 (DE-599)DOAJ4558f2f028fa475fb50028bca63872a4 DE-627 ger DE-627 rakwb eng TA1-2040 Haci Mehmet Baskonus verfasserin aut Complex mixed dark-bright wave patterns to the modified α and modified Vakhnenko-Parkes equations 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we present the sine-Gordon expansion method to prepare the mixed dark bright wave patterns to the nonlinear partial differential equations arising in mathematical physics. Then, we apply the proposed method for a credible recourse of two nonlinear physical models: the modified Vakhnenko-Parkes and modified α-equation. These exact solutions comprise the hyperbolic, trigonometric, rational and exponential function with few licentious parameter. The analytical solutions have different physical structures and they are graphically analyzed in order to show their dynamical behavior by means of 2D, 3D and contour plots. 35Axx 35Lxx 35Qxx Engineering (General). Civil engineering (General) Juan Luis García Guirao verfasserin aut Ajay Kumar verfasserin aut Fernando S. Vidal Causanilles verfasserin aut German Rodriguez Bermudez verfasserin aut In Alexandria Engineering Journal Elsevier, 2016 59(2020), 4, Seite 2149-2160 (DE-627)669887609 (DE-600)2631413-7 20902670 nnns volume:59 year:2020 number:4 pages:2149-2160 https://doi.org/10.1016/j.aej.2020.01.032 kostenfrei https://doaj.org/article/4558f2f028fa475fb50028bca63872a4 kostenfrei http://www.sciencedirect.com/science/article/pii/S1110016820300338 kostenfrei https://doaj.org/toc/1110-0168 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 59 2020 4 2149-2160
allfieldsSound	10.1016/j.aej.2020.01.032 doi (DE-627)DOAJ001753509 (DE-599)DOAJ4558f2f028fa475fb50028bca63872a4 DE-627 ger DE-627 rakwb eng TA1-2040 Haci Mehmet Baskonus verfasserin aut Complex mixed dark-bright wave patterns to the modified α and modified Vakhnenko-Parkes equations 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we present the sine-Gordon expansion method to prepare the mixed dark bright wave patterns to the nonlinear partial differential equations arising in mathematical physics. Then, we apply the proposed method for a credible recourse of two nonlinear physical models: the modified Vakhnenko-Parkes and modified α-equation. These exact solutions comprise the hyperbolic, trigonometric, rational and exponential function with few licentious parameter. The analytical solutions have different physical structures and they are graphically analyzed in order to show their dynamical behavior by means of 2D, 3D and contour plots. 35Axx 35Lxx 35Qxx Engineering (General). Civil engineering (General) Juan Luis García Guirao verfasserin aut Ajay Kumar verfasserin aut Fernando S. Vidal Causanilles verfasserin aut German Rodriguez Bermudez verfasserin aut In Alexandria Engineering Journal Elsevier, 2016 59(2020), 4, Seite 2149-2160 (DE-627)669887609 (DE-600)2631413-7 20902670 nnns volume:59 year:2020 number:4 pages:2149-2160 https://doi.org/10.1016/j.aej.2020.01.032 kostenfrei https://doaj.org/article/4558f2f028fa475fb50028bca63872a4 kostenfrei http://www.sciencedirect.com/science/article/pii/S1110016820300338 kostenfrei https://doaj.org/toc/1110-0168 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 59 2020 4 2149-2160
language	English
source	In Alexandria Engineering Journal 59(2020), 4, Seite 2149-2160 volume:59 year:2020 number:4 pages:2149-2160
sourceStr	In Alexandria Engineering Journal 59(2020), 4, Seite 2149-2160 volume:59 year:2020 number:4 pages:2149-2160
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	35Axx 35Lxx 35Qxx Engineering (General). Civil engineering (General)
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container_title	Alexandria Engineering Journal
authorswithroles_txt_mv	Haci Mehmet Baskonus @@aut@@ Juan Luis García Guirao @@aut@@ Ajay Kumar @@aut@@ Fernando S. Vidal Causanilles @@aut@@ German Rodriguez Bermudez @@aut@@
publishDateDaySort_date	2020-01-01T00:00:00Z
hierarchy_top_id	669887609
id	DOAJ001753509
language_de	englisch
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callnumber-first	T - Technology
author	Haci Mehmet Baskonus
spellingShingle	Haci Mehmet Baskonus misc TA1-2040 misc 35Axx misc 35Lxx misc 35Qxx misc Engineering (General). Civil engineering (General) Complex mixed dark-bright wave patterns to the modified α and modified Vakhnenko-Parkes equations
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title	Complex mixed dark-bright wave patterns to the modified α and modified Vakhnenko-Parkes equations
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title_full	Complex mixed dark-bright wave patterns to the modified α and modified Vakhnenko-Parkes equations
author_sort	Haci Mehmet Baskonus
journal	Alexandria Engineering Journal
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author_browse	Haci Mehmet Baskonus Juan Luis García Guirao Ajay Kumar Fernando S. Vidal Causanilles German Rodriguez Bermudez
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title_sort	complex mixed dark-bright wave patterns to the modified α and modified vakhnenko-parkes equations
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title_auth	Complex mixed dark-bright wave patterns to the modified α and modified Vakhnenko-Parkes equations
abstract	In this paper, we present the sine-Gordon expansion method to prepare the mixed dark bright wave patterns to the nonlinear partial differential equations arising in mathematical physics. Then, we apply the proposed method for a credible recourse of two nonlinear physical models: the modified Vakhnenko-Parkes and modified α-equation. These exact solutions comprise the hyperbolic, trigonometric, rational and exponential function with few licentious parameter. The analytical solutions have different physical structures and they are graphically analyzed in order to show their dynamical behavior by means of 2D, 3D and contour plots.
abstractGer	In this paper, we present the sine-Gordon expansion method to prepare the mixed dark bright wave patterns to the nonlinear partial differential equations arising in mathematical physics. Then, we apply the proposed method for a credible recourse of two nonlinear physical models: the modified Vakhnenko-Parkes and modified α-equation. These exact solutions comprise the hyperbolic, trigonometric, rational and exponential function with few licentious parameter. The analytical solutions have different physical structures and they are graphically analyzed in order to show their dynamical behavior by means of 2D, 3D and contour plots.
abstract_unstemmed	In this paper, we present the sine-Gordon expansion method to prepare the mixed dark bright wave patterns to the nonlinear partial differential equations arising in mathematical physics. Then, we apply the proposed method for a credible recourse of two nonlinear physical models: the modified Vakhnenko-Parkes and modified α-equation. These exact solutions comprise the hyperbolic, trigonometric, rational and exponential function with few licentious parameter. The analytical solutions have different physical structures and they are graphically analyzed in order to show their dynamical behavior by means of 2D, 3D and contour plots.
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title_short	Complex mixed dark-bright wave patterns to the modified α and modified Vakhnenko-Parkes equations
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Complex mixed dark-bright wave patterns to the modified α and modified Vakhnenko-Parkes equations

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