The initial-value problem for a Gardner-type equation
Discussed here is a regularized version(0.1)ut+ux+uux+Au2ux−uxxt=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}-{u}_{\mathit{xxt}}=0,$$ of the classical Gardner equationut+ux+uux+Au2ux+uxxx=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}+{u}_{\mathit{xxx}}=0,$$ that arises in hydrodynamics and plasma p...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-06-01
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| Series: | Advanced Nonlinear Studies |
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| Online Access: | https://doi.org/10.1515/ans-2023-0182 |
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| author | Bona Jerry Chen Hongqiu Guerrero Pamela Haidau Cristina Pantic Sanja |
| author_facet | Bona Jerry Chen Hongqiu Guerrero Pamela Haidau Cristina Pantic Sanja |
| author_sort | Bona Jerry |
| collection | DOAJ |
| description | Discussed here is a regularized version(0.1)ut+ux+uux+Au2ux−uxxt=0,
$${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}-{u}_{\mathit{xxt}}=0,$$
of the classical Gardner equationut+ux+uux+Au2ux+uxxx=0,
$${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}+{u}_{\mathit{xxx}}=0,$$
that arises in hydrodynamics and plasma physics. Considered here are well-posedness issues for the initial-value problem for the regularized equation posed on all of R
$\mathbb{R}$
. |
| format | Article |
| id | doaj-art-584fd2b63f8d4dcc835ce49d742be907 |
| institution | Kabale University |
| issn | 2169-0375 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj-art-584fd2b63f8d4dcc835ce49d742be9072025-08-20T03:28:18ZengDe GruyterAdvanced Nonlinear Studies2169-03752025-06-0125240942110.1515/ans-2023-0182The initial-value problem for a Gardner-type equationBona Jerry0Chen Hongqiu1Guerrero Pamela2Haidau Cristina3Pantic Sanja4Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S. Morgan Street. M/C 249, Chicago, IL60607, USADepartment of Mathematical Sciences, University of Memphis, Memphis, TN38152, USADepartment of Mathematical Sciences, University of Memphis, Memphis, TN38152, USADepartment of Mathematics and Computer Science, Lake Forest College, Lake Forest, IL60045, USADepartment of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA24061, USADiscussed here is a regularized version(0.1)ut+ux+uux+Au2ux−uxxt=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}-{u}_{\mathit{xxt}}=0,$$ of the classical Gardner equationut+ux+uux+Au2ux+uxxx=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}+{u}_{\mathit{xxx}}=0,$$ that arises in hydrodynamics and plasma physics. Considered here are well-posedness issues for the initial-value problem for the regularized equation posed on all of R $\mathbb{R}$ .https://doi.org/10.1515/ans-2023-0182gardner equationbore propagationlong-wave modelsunidirectional water-wave modelsplasma physics models30d1030d1530h9935b4435b6535e1535q5135q53 |
| spellingShingle | Bona Jerry Chen Hongqiu Guerrero Pamela Haidau Cristina Pantic Sanja The initial-value problem for a Gardner-type equation Advanced Nonlinear Studies gardner equation bore propagation long-wave models unidirectional water-wave models plasma physics models 30d10 30d15 30h99 35b44 35b65 35e15 35q51 35q53 |
| title | The initial-value problem for a Gardner-type equation |
| title_full | The initial-value problem for a Gardner-type equation |
| title_fullStr | The initial-value problem for a Gardner-type equation |
| title_full_unstemmed | The initial-value problem for a Gardner-type equation |
| title_short | The initial-value problem for a Gardner-type equation |
| title_sort | initial value problem for a gardner type equation |
| topic | gardner equation bore propagation long-wave models unidirectional water-wave models plasma physics models 30d10 30d15 30h99 35b44 35b65 35e15 35q51 35q53 |
| url | https://doi.org/10.1515/ans-2023-0182 |
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