Theory and Modern Applications
From: Symmetry reductions of the \((3+1)\)-dimensional modified Zakharov–Kuznetsov equation
\(\mathcal{V}_{1}\) | \(\mathcal{V}_{2}\) | \(\mathcal{V}_{3}\) | \(\mathcal{V}_{4}\) | \(\mathcal{V}_{5}\) | \(\mathcal{V}_{6}\) | |
---|---|---|---|---|---|---|
\(\mathcal{V}_{1}\) | \(\mathcal{V}_{1}\) | \(\Delta _{1} \) | \(e^{\frac{\varepsilon }{3}}\mathcal{V}_{3}\) | \(\mathcal{V}_{4}\) | \(e^{\frac{\varepsilon }{3}}\mathcal{V}_{5}\) | \(e^{\frac{\varepsilon }{3}}\mathcal{V}_{6}\) |
\(\mathcal{V}_{2}\) | \(\mathcal{V}_{1}-\varepsilon \mathcal{V}_{2}+\frac{2k}{3}\varepsilon \mathcal{V}_{3}\) | \(\mathcal{V}_{2}\) | \(\mathcal{V}_{3}\) | \(\mathcal{V}_{4}\) | \(\mathcal{V}_{5}\) | \(\mathcal{V}_{6}\) |
\(\mathcal{V}_{3}\) | \(\mathcal{V}_{1}-\frac{\varepsilon }{3}\mathcal{V}_{3}\) | \(\mathcal{V}_{2}\) | \(\mathcal{V}_{3}\) | \(\mathcal{V}_{4}\) | \(\mathcal{V}_{5}\) | \(\mathcal{V}_{6}\) |
\(\mathcal{V}_{4}\) | \(\mathcal{V}_{1}\) | \(\mathcal{V}_{2}\) | \(\mathcal{V}_{3}\) | \(\mathcal{V}_{4}\) | \(\Delta _{2} \) | \(\Delta _{3} \) |
\(\mathcal{V}_{5}\) | \(\mathcal{V}_{1}-\frac{1}{3}\varepsilon \mathcal{V}_{5}\) | \(\mathcal{V}_{2}\) | \(\mathcal{V}_{3}\) | \(\mathcal{V}_{4}+\varepsilon \mathcal{V}_{6}\) | \(\mathcal{V}_{5}\) | \(\mathcal{V}_{6}\) |
\(\mathcal{V}_{6}\) | \(\mathcal{V}_{1}-\frac{1}{3}\varepsilon \mathcal{V}_{6}\) | \(\mathcal{V}_{2}\) | \(\mathcal{V}_{3}\) | \(\mathcal{V}_{4}-\varepsilon \mathcal{V}_{5}\) | \(\mathcal{V}_{5}\) | \(\mathcal{V}_{6}\) |