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Volume 7, Issue 1
A General Korteweg-de Vries-Burgers Equation: Novel Ideas and Novel Results

Linghai Zhang

DOI: 10.12150/jnma.2025.334

J. Nonl. Mod. Anal., 7 (2025), pp. 334-382.

Published online: 2025-02

[An open-access article; the PDF is free to any online user.]

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  • Abstract

We consider the Cauchy problem for a general Korteweg-de Vries-Burgers equation and the Cauchy problem for the corresponding linear equation. We will couple together a few novel ideas, several existing ideas and existing results and use rigorous mathematical analysis to accomplish several very important and very interesting results for these Cauchy problems.

  • Keywords

General Korteweg-de Vries-Burgers equation, global smooth solution, existence and uniqueness, sharp rate decay estimates, exact limits, optimal decay estimates.

  • AMS Subject Headings

35Q20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-334, author = {Zhang , Linghai}, title = {A General Korteweg-de Vries-Burgers Equation: Novel Ideas and Novel Results}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {1}, pages = {334--382}, abstract = {

We consider the Cauchy problem for a general Korteweg-de Vries-Burgers equation and the Cauchy problem for the corresponding linear equation. We will couple together a few novel ideas, several existing ideas and existing results and use rigorous mathematical analysis to accomplish several very important and very interesting results for these Cauchy problems.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.334}, url = {http://global-sci.org/intro/article_detail/jnma/23829.html} }
TY - JOUR T1 - A General Korteweg-de Vries-Burgers Equation: Novel Ideas and Novel Results AU - Zhang , Linghai JO - Journal of Nonlinear Modeling and Analysis VL - 1 SP - 334 EP - 382 PY - 2025 DA - 2025/02 SN - 7 DO - http://doi.org/10.12150/jnma.2025.334 UR - https://global-sci.org/intro/article_detail/jnma/23829.html KW - General Korteweg-de Vries-Burgers equation, global smooth solution, existence and uniqueness, sharp rate decay estimates, exact limits, optimal decay estimates. AB -

We consider the Cauchy problem for a general Korteweg-de Vries-Burgers equation and the Cauchy problem for the corresponding linear equation. We will couple together a few novel ideas, several existing ideas and existing results and use rigorous mathematical analysis to accomplish several very important and very interesting results for these Cauchy problems.

Zhang , Linghai. (2025). A General Korteweg-de Vries-Burgers Equation: Novel Ideas and Novel Results. Journal of Nonlinear Modeling and Analysis. 7 (1). 334-382. doi:10.12150/jnma.2025.334
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