Be careful with variable separation solutions via the extended tanh-function method and periodic wave structures

We analyze the extended tanh-function method to realize variable separation, however, we find that various "different" solutions obtained by this method are seriously equivalent to the general solution derived by the multilinear variable separation approach. In order to illustrate this poi...
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Gespeichert in:

Autor*in:	Chaoqing Dai [verfasserIn] Qin Liu [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2015

Schlagwörter:	extended tanh-function method uniform variable separation solutions general (2 1)-dimensional Korteweg–de Vries system periodic localized coherent structures

Übergeordnetes Werk:	In: Nonlinear Analysis - Vilnius University Press, 2019, 20(2015), 4
Übergeordnetes Werk:	volume:20 ; year:2015 ; number:4

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc Journal toc

DOI / URN:	10.15388/NA.2015.4.2

Katalog-ID:	DOAJ065504399

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allfields	10.15388/NA.2015.4.2 doi (DE-627)DOAJ065504399 (DE-599)DOAJf8074bd9cc3c4fe993a2d8fd3b258b56 DE-627 ger DE-627 rakwb eng QA299.6-433 Chaoqing Dai verfasserin aut Be careful with variable separation solutions via the extended tanh-function method and periodic wave structures 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We analyze the extended tanh-function method to realize variable separation, however, we find that various "different" solutions obtained by this method are seriously equivalent to the general solution derived by the multilinear variable separation approach. In order to illustrate this point, we take a general (2 + 1)-dimensional Korteweg–de Vries system in water for example. Eight kind of variable separation solutions for a general (2 + 1)-dimensional Korteweg–de Vries system are derived by means of the extended tanh-function method and the improved tanh-function method. By detailed investigation, we find that these seemly independent variable separation solutions actually depend on each other. It is verified that many of so-called "new" solutions are equivalent to one another. Based on the uniform variable separation solution, abundant localized coherent structures can be constructed. However, we must pay our attention to the solution expression of all components to avoid the appearance of some un-physical related and divergent structures: seemly abundant structures for a special component are obtained while the divergence of the corresponding other component for the same equation appears. extended tanh-function method uniform variable separation solutions general (2 1)-dimensional Korteweg–de Vries system periodic localized coherent structures Analysis Qin Liu verfasserin aut In Nonlinear Analysis Vilnius University Press, 2019 20(2015), 4 (DE-627)656866489 (DE-600)2604540-0 23358963 nnns volume:20 year:2015 number:4 https://doi.org/10.15388/NA.2015.4.2 kostenfrei https://doaj.org/article/f8074bd9cc3c4fe993a2d8fd3b258b56 kostenfrei http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13506 kostenfrei https://doaj.org/toc/1392-5113 Journal toc kostenfrei https://doaj.org/toc/2335-8963 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA 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_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 20 2015 4
spelling	10.15388/NA.2015.4.2 doi (DE-627)DOAJ065504399 (DE-599)DOAJf8074bd9cc3c4fe993a2d8fd3b258b56 DE-627 ger DE-627 rakwb eng QA299.6-433 Chaoqing Dai verfasserin aut Be careful with variable separation solutions via the extended tanh-function method and periodic wave structures 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We analyze the extended tanh-function method to realize variable separation, however, we find that various "different" solutions obtained by this method are seriously equivalent to the general solution derived by the multilinear variable separation approach. In order to illustrate this point, we take a general (2 + 1)-dimensional Korteweg–de Vries system in water for example. Eight kind of variable separation solutions for a general (2 + 1)-dimensional Korteweg–de Vries system are derived by means of the extended tanh-function method and the improved tanh-function method. By detailed investigation, we find that these seemly independent variable separation solutions actually depend on each other. It is verified that many of so-called "new" solutions are equivalent to one another. Based on the uniform variable separation solution, abundant localized coherent structures can be constructed. However, we must pay our attention to the solution expression of all components to avoid the appearance of some un-physical related and divergent structures: seemly abundant structures for a special component are obtained while the divergence of the corresponding other component for the same equation appears. extended tanh-function method uniform variable separation solutions general (2 1)-dimensional Korteweg–de Vries system periodic localized coherent structures Analysis Qin Liu verfasserin aut In Nonlinear Analysis Vilnius University Press, 2019 20(2015), 4 (DE-627)656866489 (DE-600)2604540-0 23358963 nnns volume:20 year:2015 number:4 https://doi.org/10.15388/NA.2015.4.2 kostenfrei https://doaj.org/article/f8074bd9cc3c4fe993a2d8fd3b258b56 kostenfrei http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13506 kostenfrei https://doaj.org/toc/1392-5113 Journal toc kostenfrei https://doaj.org/toc/2335-8963 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA 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_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 20 2015 4
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allfieldsGer	10.15388/NA.2015.4.2 doi (DE-627)DOAJ065504399 (DE-599)DOAJf8074bd9cc3c4fe993a2d8fd3b258b56 DE-627 ger DE-627 rakwb eng QA299.6-433 Chaoqing Dai verfasserin aut Be careful with variable separation solutions via the extended tanh-function method and periodic wave structures 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We analyze the extended tanh-function method to realize variable separation, however, we find that various "different" solutions obtained by this method are seriously equivalent to the general solution derived by the multilinear variable separation approach. In order to illustrate this point, we take a general (2 + 1)-dimensional Korteweg–de Vries system in water for example. Eight kind of variable separation solutions for a general (2 + 1)-dimensional Korteweg–de Vries system are derived by means of the extended tanh-function method and the improved tanh-function method. By detailed investigation, we find that these seemly independent variable separation solutions actually depend on each other. It is verified that many of so-called "new" solutions are equivalent to one another. Based on the uniform variable separation solution, abundant localized coherent structures can be constructed. However, we must pay our attention to the solution expression of all components to avoid the appearance of some un-physical related and divergent structures: seemly abundant structures for a special component are obtained while the divergence of the corresponding other component for the same equation appears. extended tanh-function method uniform variable separation solutions general (2 1)-dimensional Korteweg–de Vries system periodic localized coherent structures Analysis Qin Liu verfasserin aut In Nonlinear Analysis Vilnius University Press, 2019 20(2015), 4 (DE-627)656866489 (DE-600)2604540-0 23358963 nnns volume:20 year:2015 number:4 https://doi.org/10.15388/NA.2015.4.2 kostenfrei https://doaj.org/article/f8074bd9cc3c4fe993a2d8fd3b258b56 kostenfrei http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13506 kostenfrei https://doaj.org/toc/1392-5113 Journal toc kostenfrei https://doaj.org/toc/2335-8963 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA 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_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 20 2015 4
allfieldsSound	10.15388/NA.2015.4.2 doi (DE-627)DOAJ065504399 (DE-599)DOAJf8074bd9cc3c4fe993a2d8fd3b258b56 DE-627 ger DE-627 rakwb eng QA299.6-433 Chaoqing Dai verfasserin aut Be careful with variable separation solutions via the extended tanh-function method and periodic wave structures 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We analyze the extended tanh-function method to realize variable separation, however, we find that various "different" solutions obtained by this method are seriously equivalent to the general solution derived by the multilinear variable separation approach. In order to illustrate this point, we take a general (2 + 1)-dimensional Korteweg–de Vries system in water for example. Eight kind of variable separation solutions for a general (2 + 1)-dimensional Korteweg–de Vries system are derived by means of the extended tanh-function method and the improved tanh-function method. By detailed investigation, we find that these seemly independent variable separation solutions actually depend on each other. It is verified that many of so-called "new" solutions are equivalent to one another. Based on the uniform variable separation solution, abundant localized coherent structures can be constructed. However, we must pay our attention to the solution expression of all components to avoid the appearance of some un-physical related and divergent structures: seemly abundant structures for a special component are obtained while the divergence of the corresponding other component for the same equation appears. extended tanh-function method uniform variable separation solutions general (2 1)-dimensional Korteweg–de Vries system periodic localized coherent structures Analysis Qin Liu verfasserin aut In Nonlinear Analysis Vilnius University Press, 2019 20(2015), 4 (DE-627)656866489 (DE-600)2604540-0 23358963 nnns volume:20 year:2015 number:4 https://doi.org/10.15388/NA.2015.4.2 kostenfrei https://doaj.org/article/f8074bd9cc3c4fe993a2d8fd3b258b56 kostenfrei http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13506 kostenfrei https://doaj.org/toc/1392-5113 Journal toc kostenfrei https://doaj.org/toc/2335-8963 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA 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_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 20 2015 4
language	English
source	In Nonlinear Analysis 20(2015), 4 volume:20 year:2015 number:4
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topic_facet	extended tanh-function method uniform variable separation solutions general (2 1)-dimensional Korteweg–de Vries system periodic localized coherent structures Analysis
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container_title	Nonlinear Analysis
authorswithroles_txt_mv	Chaoqing Dai @@aut@@ Qin Liu @@aut@@
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callnumber-first	Q - Science
author	Chaoqing Dai
spellingShingle	Chaoqing Dai misc QA299.6-433 misc extended tanh-function method misc uniform variable separation solutions misc general (2 1)-dimensional Korteweg–de Vries system misc periodic localized coherent structures misc Analysis Be careful with variable separation solutions via the extended tanh-function method and periodic wave structures
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topic_title	QA299.6-433 Be careful with variable separation solutions via the extended tanh-function method and periodic wave structures extended tanh-function method uniform variable separation solutions general (2 1)-dimensional Korteweg–de Vries system periodic localized coherent structures
topic	misc QA299.6-433 misc extended tanh-function method misc uniform variable separation solutions misc general (2 1)-dimensional Korteweg–de Vries system misc periodic localized coherent structures misc Analysis
topic_unstemmed	misc QA299.6-433 misc extended tanh-function method misc uniform variable separation solutions misc general (2 1)-dimensional Korteweg–de Vries system misc periodic localized coherent structures misc Analysis
topic_browse	misc QA299.6-433 misc extended tanh-function method misc uniform variable separation solutions misc general (2 1)-dimensional Korteweg–de Vries system misc periodic localized coherent structures misc Analysis
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title	Be careful with variable separation solutions via the extended tanh-function method and periodic wave structures
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title_sort	be careful with variable separation solutions via the extended tanh-function method and periodic wave structures
callnumber	QA299.6-433
title_auth	Be careful with variable separation solutions via the extended tanh-function method and periodic wave structures
abstract	We analyze the extended tanh-function method to realize variable separation, however, we find that various "different" solutions obtained by this method are seriously equivalent to the general solution derived by the multilinear variable separation approach. In order to illustrate this point, we take a general (2 + 1)-dimensional Korteweg–de Vries system in water for example. Eight kind of variable separation solutions for a general (2 + 1)-dimensional Korteweg–de Vries system are derived by means of the extended tanh-function method and the improved tanh-function method. By detailed investigation, we find that these seemly independent variable separation solutions actually depend on each other. It is verified that many of so-called "new" solutions are equivalent to one another. Based on the uniform variable separation solution, abundant localized coherent structures can be constructed. However, we must pay our attention to the solution expression of all components to avoid the appearance of some un-physical related and divergent structures: seemly abundant structures for a special component are obtained while the divergence of the corresponding other component for the same equation appears.
abstractGer	We analyze the extended tanh-function method to realize variable separation, however, we find that various "different" solutions obtained by this method are seriously equivalent to the general solution derived by the multilinear variable separation approach. In order to illustrate this point, we take a general (2 + 1)-dimensional Korteweg–de Vries system in water for example. Eight kind of variable separation solutions for a general (2 + 1)-dimensional Korteweg–de Vries system are derived by means of the extended tanh-function method and the improved tanh-function method. By detailed investigation, we find that these seemly independent variable separation solutions actually depend on each other. It is verified that many of so-called "new" solutions are equivalent to one another. Based on the uniform variable separation solution, abundant localized coherent structures can be constructed. However, we must pay our attention to the solution expression of all components to avoid the appearance of some un-physical related and divergent structures: seemly abundant structures for a special component are obtained while the divergence of the corresponding other component for the same equation appears.
abstract_unstemmed	We analyze the extended tanh-function method to realize variable separation, however, we find that various "different" solutions obtained by this method are seriously equivalent to the general solution derived by the multilinear variable separation approach. In order to illustrate this point, we take a general (2 + 1)-dimensional Korteweg–de Vries system in water for example. Eight kind of variable separation solutions for a general (2 + 1)-dimensional Korteweg–de Vries system are derived by means of the extended tanh-function method and the improved tanh-function method. By detailed investigation, we find that these seemly independent variable separation solutions actually depend on each other. It is verified that many of so-called "new" solutions are equivalent to one another. Based on the uniform variable separation solution, abundant localized coherent structures can be constructed. However, we must pay our attention to the solution expression of all components to avoid the appearance of some un-physical related and divergent structures: seemly abundant structures for a special component are obtained while the divergence of the corresponding other component for the same equation appears.
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title_short	Be careful with variable separation solutions via the extended tanh-function method and periodic wave structures
url	https://doi.org/10.15388/NA.2015.4.2 https://doaj.org/article/f8074bd9cc3c4fe993a2d8fd3b258b56 http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13506 https://doaj.org/toc/1392-5113 https://doaj.org/toc/2335-8963
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Be careful with variable separation solutions via the extended tanh-function method and periodic wave structures

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