Correction to: Coupled nonlinear Schrödinger (CNLS) equations for two interacting electrostatic wavepackets in a non-Maxwellian fluid plasma model

Correction to: Nonlinear Dyn (2024) 112:2795–2819https://doi.org/10.1007/s11071-023-09165-4

The authors regret to have to point out that a few typographical errors slipped through their article [N. Lazarides and I. Kourakis, Nonlinear Dynamics (2024) 112:2795–2819].

It is emphasized that the errors are limited to the respective algebraic relations where they appear, and that the results reported in the article remain entirely unaffected by these errors.

• 1. In page 2806 (right column) Eqs. (70) in our article

  $$\begin{aligned} \Psi _j =( \Psi _{j,0} +\varepsilon _j ) \, e^{i \phi _j \tau }, \end{aligned}$$

  should read

  $$\begin{aligned} \Psi _j =( \Psi _{j,0} +\varepsilon _j ) \, e^{i {\tilde{\omega }}_j \tau }, \end{aligned}$$

  i.e., $\phi _j$ in Eq. (70) should be replaced by ${\tilde{\omega }}_j$ defined in Eqs. (68) and (69).

• 2. In page 2806 (right column) Eqs. (71) and (72) in our article

  $$\begin{aligned}{} & {} i \left( \frac{\partial \varepsilon _1}{\partial \tau } +\delta \frac{\partial \varepsilon _1}{\partial \xi } \right) +\Psi _{1,0} \phi _1 +P_1 \frac{\partial ^2 \varepsilon _1}{\partial \xi ^2}\\{} & {} \quad +Q_{11} \Psi _{1,0}^2 (\varepsilon _1 +\varepsilon _1^\star ) +Q_{12} {\Psi }_{1,0} \Psi _{2,0} (\varepsilon _2 +\varepsilon _2^\star ) =0, \\{} & {} i \left( \frac{\partial \varepsilon _2}{\partial \tau } -\delta \frac{\partial \varepsilon _2}{\partial \xi } \right) +\Psi _{2,0} \phi _2 +P_2 \frac{\partial ^2 \varepsilon _2}{\partial \xi ^2}\\{} & {} \quad +Q_{22} \Psi _{2,0}^2 (\varepsilon _2 +\varepsilon _2^\star ) +Q_{21} \Psi _{2,0} \Psi _{1,0} (\varepsilon _1 +\varepsilon _1^\star ) =0. \end{aligned}$$

  should read

  $$\begin{aligned}{} & {} i \left( \frac{\partial \varepsilon _1}{\partial \tau } +\delta \frac{\partial \varepsilon _1}{\partial \xi } \right) +P_1 \frac{\partial ^2 \varepsilon _1}{\partial \xi ^2}\\{} & {} \quad +Q_{11} \Psi _{1,0}^2 (\varepsilon _1 +\varepsilon _1^\star ) +Q_{12} {\Psi }_{1,0} \Psi _{2,0} (\varepsilon _2 +\varepsilon _2^\star ) =0, \\{} & {} i \left( \frac{\partial \varepsilon _2}{\partial \tau } -\delta \frac{\partial \varepsilon _2}{\partial \xi } \right) +P_2 \frac{\partial ^2 \varepsilon _2}{\partial \xi ^2}\\{} & {} \quad +Q_{22} \Psi _{2,0}^2 (\varepsilon _2 +\varepsilon _2^\star ) +Q_{21} \Psi _{2,0} \Psi _{1,0} (\varepsilon _1 +\varepsilon _1^\star ) =0. \end{aligned}$$

  i.e, the terms $\Psi _{1,0} \phi _1$ and $\Psi _{1,0} \phi _2$ should be absent.

• 3. In page 2806 (right column) Eq. (75) in our article

  $$\begin{aligned} g_j(\xi ,\tau ) =g_{j,0} \, e^{i (K \xi -\Omega \tau )}, \end{aligned}$$

  should read

  $$\begin{aligned} g_j(\xi ,\tau ) =g_{j,0} \, e^{i (K \xi -\Omega \tau )} \, + c.c., \end{aligned}$$

  where “c.c.” denotes the complex conjugate. The addition of the complex conjugate to $g_j$ makes that quantity real, as it should read(as per its definition as the real part of $\varepsilon _j$ in the two lines following Eq. (72) in our article.

• 4. In page 2806 (right column) Eq. (78) in our article,

  $$\begin{aligned} \Omega _c^4 =4 P_1 P_2 Q_{12} Q_{21} \Psi _{1,0}^2 \Psi _{2,0}^2, \end{aligned}$$

  should instead read

  $$\begin{aligned} \Omega _c^4 =4 P_1 P_2 Q_{12} Q_{21} \Psi _{1,0}^2 \Psi _{2,0}^2 \, K^4. \end{aligned}$$