## Domain wall solutions of KdV like equations with higher order nonlinearity.(English)Zbl 0624.35070

This paper deals with the exact domain wall (kink) solutions of the Korteweg-de Vries (KdV) like nonlinear partial differential equations with higher order nonlinearity. Four forms of these equations are examined, i.e.: $(i)\quad u_ t+a(1+bu)uu_ x+du_{xxx}=0,\quad a;d>0,\quad (ii)\quad [a(1+bu)u-\eta]u_ x+du_{xxx}=0,\quad \eta /a;\quad \eta /d>0,$
$(iii)\quad u_ t+bu^ 2u_ x- du_{xxx}=0,\quad b;d>0,\quad (iv)\quad u_ t+a(1+bu^ 2)u^ 2u_ x+du_{xxx}=0,\quad a;d>0.$ The solutions are compared with the standard known solution of the $$\lambda \phi^{2n}$$ field theories. Some conservation laws for these system of equations are also given.
Reviewer: D.E.Panayotounakos

### MSC:

 35Q99 Partial differential equations of mathematical physics and other areas of application 35G20 Nonlinear higher-order PDEs 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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