# Equation index

• Boussinesq equation

${u}_{tt}={u}_{xx}+\sigma {\left({u}^{2}\right)}_{xx}+\beta {u}_{xxxx}$

• Burgers' equation

${u}_{t}+\alpha u{u}_{x}=\mu {u}_{xx}$

• Burgers' hierarchy

${u}_{t}+\alpha \frac{\partial }{\partial x}{\left(\frac{\partial }{\partial x}+u\right)}^{n}u=0,\text{ }n=0, 1, 2,\dots$

• Ginzburg-Landau equation

${A}_{t}=\left(1+ib\right)\Delta A+\epsilon A-\left(1-ic\right){|A|}^{2}A$

$\frac{\partial }{\partial x}\left({u}_{t}+u{u}_{x}+\beta {u}_{xxx}\right)+3{\delta }^{2}{u}_{yy}=0$

• Korteweg-de Vries equation

${u}_{t}+6u{u}_{x}+{u}_{xxx}=0$

• Korteweg-de Vries hierarchy

${u}_{t}+\frac{\partial }{\partial x}{L}_{n+1}\left[u\right]=0,$

• Kuramoto-Sivashinsky equation

${u}_{t}+u{u}_{x}+\alpha {u}_{xx}+\beta {u}_{xxx}+\gamma {u}_{xxxx}=0$

• Modified Korteweg-de Vries equation

${u}_{t}-6{u}^{2}{u}_{x}+{u}_{xxx}=0$

• Modified Korteweg-de Vries hierarchy

${u}_{t}+\frac{\partial }{\partial x}\left(\frac{\partial }{\partial x}+2u\right){L}_{n}\left[{u}_{x}-{u}^{2}\right]=0,$

• Nonlinear Schrodinger equation

$i\frac{\partial a}{\partial t}=3k\frac{{\partial }^{2}a}{\partial {x}^{2}}+ka{|a|}^{2}$

• Nonlinear transport equation

${u}_{t}+u{u}_{x}=0$

• Sharma-Tasso-Olver equation

${u}_{t}+\alpha {u}_{xxx}+\frac{3}{2}\alpha {\left({u}^{2}\right)}_{xx}+\alpha {\left({u}^{3}\right)}_{x}=0$

• Sine-Gordon equation

${\phi }_{tt}-{\phi }_{xx}+\mathrm{sin}\phi =0\text{ }or\text{ }{u}_{\xi \tau }=\mathrm{sin}u$