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2.15 Nonlinear PDE’s

2.15.1 Bateman-Burgers \(u_t+u u_x = \nu u_{xx}\)
2.15.2 Benjamin Bona Mahony \(u_t+u_x + u u+x - u_{xxt} = 0\)
2.15.3 Benjamin Ono \(u_t+H u_{xx} +u u_x = 0\)
2.15.4 Born Infeld \((1-u_t^2) u_{xx} + 2 u_x u_t u_{xt} - (1+ u_x^2) u_{tt}=0\)
2.15.5 Boussinesq \(u_{tt}-u_{xx}-u_{xxxx} - 3 (u^2)_{xx} = 0\)
2.15.6 Boussinesq type \(u_{tt}-u_{xx}-2 \alpha (u u_x)_x - \beta u_{xxtt} = 0\)
2.15.7 Buckmaster \( u_t = (u^4)_{xx} + (u^3)_x\)
2.15.8 Camassa Holm \(u_t + 2 k u_x - u_{xxt} + 3 u u_x = 2 u_x u_{xx}+ u u_{xxx}\)
2.15.9 Chaffee Infante \(u_t = u_{xx} + \lambda (u^3 - u) = 0\)
2.15.10 Clarke. \(\left ( \theta _t - \gamma e^\theta \right )_{tt} = \left ( \theta _t - e^\theta \right )_{xx}\)
2.15.11 Degasperis Procesi \(u_t - u_{xxt} + 4 u u_x = 3 u_x u_xx + u u_{xxx}\)
2.15.12 Dym equation \(u_t =u^3 u_{xxx}\)
2.15.13 Estevez Mansfield Clarkson \(u_{tyyy} + \beta u_y u_{yt} + \beta u_{yy} u_t + u_{tt} = 0\)
2.15.14 Fisher’s \(u_t = u(1-u)+u_{xx}\)
2.15.15 Hunter Saxton \(\left ( u_t + u u_x) \right )_x = \frac {1}{2} (u_x)^2\)
2.15.16 Kadomtsev Petviashvili \( \left ( u_t + u u_x + \epsilon ^2 u_{xxx} \right )_x + \lambda u_{yy} = 0 \)
2.15.17 Klein Gordon \(u_{xx}+u_{yy}+ \lambda u^p=0\)
2.15.18 Klein Gordon \(u_{xx}+u_{yy}+ u^2=0\)
2.15.19 Khokhlov Zabolotskaya \(u_{x t} - (u u_x)_x = u_{yy}\)
2.15.20 Korteweg de Vries (KdV) \(u_t + (u_x)^3+ 6 u u_x = 0\)
2.15.21 Lin Tsien \(2 u_{tx} + u_x u_{xx} - u_{yy} = 0\)
2.15.22 Liouville \(u_{xx} + u_{yy} +e^{\lambda u} = 0\)
2.15.23 Plateau \((1+u_y^2)u_{xx} - 2 u_x u_y y_{xy} + (1+u_x^2) u_{yy} = 0\)
2.15.24 Rayleigh \(u_{tt} - u_{xx} = \epsilon (u_t - u_t^3)\)
2.15.25 Sawada Kotera \(u_t + 45 u^2 u_x + 15 u_x u_{xx} + 15 u u_{xxx} + u_{xxxxx} = 0 \)
2.15.26 Sine Gordon \(\phi _{tt} - \phi _{xx} + \sin \phi = 0\)
2.15.27 Sinh Gordon \( u_{xt} = \sinh u\)
2.15.28 Sinh Poisson \(u_{xx}+u_{yy} + \sinh u=0\)
2.15.29 Thomas equation \( u_{xy} + \alpha u_x + \beta u_y+ \nu u_x u_y =0\)
2.15.30 phi equation \(\phi _{tt} - \phi _{xx} - \phi + \phi ^3 = 0\)

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