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Volume 36, Issue 3
Invariant Subspace and Exact Solutions to the Generalized Kudryashov-Sinelshchikov Equation

Jina Li, Gaizhu Qu, Jianlin Zhang & Xuehui Ji

DOI: 10.4208/jpde.v36.n3.3

J. Part. Diff. Eq., 36 (2023), pp. 286-304.

Published online: 2023-08

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  • Abstract

In this research, invariant subspaces and exact solutions for the governing equation are obtained through the invariant subspace method, and the generalized second-order Kudryashov-Sinelshchikov equation is used to describe pressure waves in a liquid with bubbles. The governing equations are classified and transformed into a system of ordinary differential equations, and the exact solutions of the classified equation are obtained by solving the system of ordinary differential equations. The method gives logarithmic, polynomial, exponential, and trigonometric solutions for equations. The primary accomplishments of this work are displaying how to obtain the exact solutions of the classified equations and giving the stability analysis of reduced ordinary differential equations.

  • Keywords

Invariant subspace method, exact solution, Kudryashov-Sinelshchikov equation, stability analysis.

  • AMS Subject Headings

35Q53, 37K35, 37K25, 53A55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-36-286, author = {Li , JinaQu , GaizhuZhang , Jianlin and Ji , Xuehui}, title = {Invariant Subspace and Exact Solutions to the Generalized Kudryashov-Sinelshchikov Equation}, journal = {Journal of Partial Differential Equations}, year = {2023}, volume = {36}, number = {3}, pages = {286--304}, abstract = {

In this research, invariant subspaces and exact solutions for the governing equation are obtained through the invariant subspace method, and the generalized second-order Kudryashov-Sinelshchikov equation is used to describe pressure waves in a liquid with bubbles. The governing equations are classified and transformed into a system of ordinary differential equations, and the exact solutions of the classified equation are obtained by solving the system of ordinary differential equations. The method gives logarithmic, polynomial, exponential, and trigonometric solutions for equations. The primary accomplishments of this work are displaying how to obtain the exact solutions of the classified equations and giving the stability analysis of reduced ordinary differential equations.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v36.n3.3}, url = {http://global-sci.org/intro/article_detail/jpde/21889.html} }
TY - JOUR T1 - Invariant Subspace and Exact Solutions to the Generalized Kudryashov-Sinelshchikov Equation AU - Li , Jina AU - Qu , Gaizhu AU - Zhang , Jianlin AU - Ji , Xuehui JO - Journal of Partial Differential Equations VL - 3 SP - 286 EP - 304 PY - 2023 DA - 2023/08 SN - 36 DO - http://doi.org/10.4208/jpde.v36.n3.3 UR - https://global-sci.org/intro/article_detail/jpde/21889.html KW - Invariant subspace method, exact solution, Kudryashov-Sinelshchikov equation, stability analysis. AB -

In this research, invariant subspaces and exact solutions for the governing equation are obtained through the invariant subspace method, and the generalized second-order Kudryashov-Sinelshchikov equation is used to describe pressure waves in a liquid with bubbles. The governing equations are classified and transformed into a system of ordinary differential equations, and the exact solutions of the classified equation are obtained by solving the system of ordinary differential equations. The method gives logarithmic, polynomial, exponential, and trigonometric solutions for equations. The primary accomplishments of this work are displaying how to obtain the exact solutions of the classified equations and giving the stability analysis of reduced ordinary differential equations.

Li , JinaQu , GaizhuZhang , Jianlin and Ji , Xuehui. (2023). Invariant Subspace and Exact Solutions to the Generalized Kudryashov-Sinelshchikov Equation. Journal of Partial Differential Equations. 36 (3). 286-304. doi:10.4208/jpde.v36.n3.3
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