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


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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