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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.

Pierre Gaillard. (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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