Theory and Modern Applications
From: Some new exact solutions of \((3+1)\)-dimensional Burgers system via Lie symmetry analysis
\(OP_{i} \) | P | \(U_{i}\) | Similarity reduced equations |
---|---|---|---|
\(X_{3}, X_{2}, X_{5}\) | \(\frac{z}{x}\) | xu | \(\varphi ''+\varphi ''p^{2}+2p\varphi '\eta +4p\varphi '+2\varphi =2p\varphi '\psi +2\psi \varphi \) |
xv | \(\varphi 'p+\varphi =0\) | ||
xw | \(\varphi '=0\) | ||
\(X_{1}, X_{3}, X_{4}\) | \(\frac{z}{x}\) | \(\frac{x(2tu+y)}{2t}\) | \(\varphi ''+p^{2}\varphi ''+2p\varphi '\eta +4p\varphi '+2\varphi =2p\varphi '\psi +2\psi \varphi \) |
\(\frac{x(2tv+x)}{2t}\) | \(\varphi 'p+\varphi =0\) | ||
\(\frac{x(2tw+z)}{2t}\) | \(\varphi '=0\) |