Correction to: Soliton, periodic and superposition solutions to nonlocal (2 + 1)-dimensional, extended KdV equation derived from the ideal fluid model

Correction to: Nonlinear Dyn (2023) 111:18373–18389 https://doi.org/10.1007/s11071-023-08819-7

The original article was published with errors in formulas (29), (35) and (37) of the article.

In (29), there should be $\frac{1}{3}\eta_{xx} \;{\text{instead}}\;\frac{1}{3}u_{xx}$ and $- \frac{1}{2}G....\;{\text{instead}}\; - \frac{1}{2}\beta G....$ in the first row. In the second row of (29), there should be $\frac{1}{2}\eta \eta_{xx} \;{\text{instead}}\;\frac{1}{2}\eta \eta_{x}$. The last correction should also occur five lines below (29).

Formula (25) should read as:

$$\begin{aligned} w= \eta &+ \beta \left(-\frac{1}{4} A \eta^2 +\frac{1}{3} \eta_{xx} -\frac{1}{2} G \int (\int \eta_{yy}\,dx)\,dx \right) \nonumber \\ & +\beta^{2} \left( \frac{1}{8} A^2 \eta^3 +A \left(\frac{3}{16} \eta_{x}^2+\frac{1}{2} \eta \eta_{xx}\right) \right. \nonumber\\ & \left. +\frac{1}{10} \eta_{4x} +A G\, \text{Q} + G^2 \text{P} + G\, \text{R} \right) \nonumber \end{aligned}$$

(25)

Formula (35) should read as:

$$\begin{aligned} \text{Q} & = \frac{5}{8}\!\int\! ( \!\int\!(\eta_{y}^2+\eta \eta_{yy}) \,dx )\, dx -\frac{3}{8}\!\int\! (\eta \!\int\! \eta_{yy}\,dx)\,dx \nonumber \end{aligned}$$

(35)

In (37), there should be $\frac{1}{3}\eta_{xx} \;{\text{instead}}\;\frac{1}{3}u_{xx}$ and $- \frac{1}{2}G....\;{\text{instead}}\; - \frac{1}{2}\beta G....$ in the first row. In the second row, there should be $\frac{1}{2}\eta \eta_{xx} \;{\text{instead}}\;\frac{1}{2}\eta \eta_{x}$.

Formula (37) should read as:

$$\begin{aligned} w= & \eta + \beta \left(-\frac{1}{4} A \eta^2 +\frac{1}{3} \eta_{xx} -\frac{1}{2} G \int (\int \eta_{yy}\,dx)\,dx \right) \nonumber\\ & +\beta^{2} \left( A^2 \frac{1}{8} \eta^3 +A \left(\frac{3}{16} \eta_{x}^2+\frac{1}{2} \eta \eta_{xx}\right) +\frac{1}{10} \eta_{4x} \right. \nonumber\\ & +A G\, \left( \frac{5}{8}\!\int\! ( \!\int\! (\eta_{y}^2+\eta \eta_{yy}) \,dx )\,dx -\frac{3}{8}\!\int\! (\eta \!\int\! \eta_{yy}\,dx)\,dx \right) \nonumber\\ & \left. + G^2\, \frac{3}{8} \!\int\! (\!\int\! (\!\int\! (\!\int\! \eta_{4y}\,dx)\,dx)\,dx)\,dx + G\, \frac{1}{6}\, \eta_{yy} \right), \nonumber \end{aligned}$$

(37)

This correction stands to correct the original article.