1 Correction to: Journal of Dynamics and Differential Equations https://doi.org/10.1007/s10884-021-10000-w
The original version of this article unfortunately contained few typos in equations presented under proof of Proposition 3.5 section.
Initially, it was published incorrectly as
It follows from (3.11) that period L and parameter \({\mathcal {I}}\) are expressed uniquely by
where \(\alpha \) depends on k if \(c \ne 0\). Computing derivatives in k yields
If \(c > 0\) and \(k \in (\frac{1}{\sqrt{2}},1)\), then \(\frac{d {\mathcal {I}}}{dk} > 0\) and \(\frac{d L}{dk} < 0\) so that the mapping \({\mathcal {I}} \mapsto L\) is monotonically decreasing. As \(k \rightarrow \frac{1}{\sqrt{2}}\), \(\alpha \rightarrow \infty \) and \(L \rightarrow 0\). As \(k \rightarrow 1\), \(K(k) \rightarrow \infty \) and \(L \rightarrow \infty \).
If \(c < 0\) and \(k \in (0,\frac{1}{\sqrt{2}})\), then \(\frac{d \mathcal {I}}{dk} > 0\) and \(\frac{d L}{dk} < 0\) due to (3.7) and
Now, the corrected equations are presented here:
It follows from (3.11) that period L and parameter \({\mathcal {I}}\) are expressed uniquely by
where \(\alpha \) depends on k if \(c \ne 0\). Computing derivatives in k yields
If \(c > 0\) and \(k \in (\frac{1}{\sqrt{2}},1)\), then \(\frac{d {\mathcal {I}}}{dk} < 0\) and \(\frac{d L}{dk} > 0\) so that the mapping \({\mathcal {I}} \mapsto L\) is monotonically decreasing. As \(k \rightarrow \frac{1}{\sqrt{2}}\), \(\alpha \rightarrow \infty \) and \(L \rightarrow 0\). As \(k \rightarrow 1\), \(K(k) \rightarrow \infty \) and \(L \rightarrow \infty \).
If \(c < 0\) and \(k \in (0,\frac{1}{\sqrt{2}})\), then \(\frac{d \mathcal {I}}{dk} > 0\) and \(\frac{d L}{dk} < 0\) due to (3.7) and
The original article has been corrected.
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Natali, F., Le, U. & Pelinovsky, D.E. Correction to: Periodic Waves in the Fractional Modified Korteweg–de Vries Equation. J Dyn Diff Equat 34, 1641–1642 (2022). https://doi.org/10.1007/s10884-021-10016-2
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DOI: https://doi.org/10.1007/s10884-021-10016-2