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Volume 4, Issue 4
Rational Solutions to the KdV Equation in Terms of Particular Polynomials

Pierre Gaillard

DOI: 10.12150/jnma.2022.615

J. Nonl. Mod. Anal., 4 (2022), pp. 615-627.

Published online: 2023-08

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

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  • Abstract

Here, we construct rational solutions to the KdV equation by particular polynomials. We get the solutions in terms of determinants of the order $n$ for any positive integer $n,$ and we call these solutions, solutions of the order $n.$ Therefore, we obtain a very efficient method to get rational solutions to the KdV equation, and we can construct explicit solutions very easily. In the following, we present some solutions until order 10.

  • Keywords

Polynomial, Bilinear differential operator, Rational solution.

  • AMS Subject Headings

35C99, 35Q35, 35Q53

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-4-615, author = {Gaillard , Pierre}, title = {Rational Solutions to the KdV Equation in Terms of Particular Polynomials}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {4}, number = {4}, pages = {615--627}, abstract = {

Here, we construct rational solutions to the KdV equation by particular polynomials. We get the solutions in terms of determinants of the order $n$ for any positive integer $n,$ and we call these solutions, solutions of the order $n.$ Therefore, we obtain a very efficient method to get rational solutions to the KdV equation, and we can construct explicit solutions very easily. In the following, we present some solutions until order 10.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.615}, url = {http://global-sci.org/intro/article_detail/jnma/21901.html} }
TY - JOUR T1 - Rational Solutions to the KdV Equation in Terms of Particular Polynomials AU - Gaillard , Pierre JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 615 EP - 627 PY - 2023 DA - 2023/08 SN - 4 DO - http://doi.org/10.12150/jnma.2022.615 UR - https://global-sci.org/intro/article_detail/jnma/21901.html KW - Polynomial, Bilinear differential operator, Rational solution. AB -

Here, we construct rational solutions to the KdV equation by particular polynomials. We get the solutions in terms of determinants of the order $n$ for any positive integer $n,$ and we call these solutions, solutions of the order $n.$ Therefore, we obtain a very efficient method to get rational solutions to the KdV equation, and we can construct explicit solutions very easily. In the following, we present some solutions until order 10.

Gaillard , Pierre. (2023). Rational Solutions to the KdV Equation in Terms of Particular Polynomials. Journal of Nonlinear Modeling and Analysis. 4 (4). 615-627. doi:10.12150/jnma.2022.615
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