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An exact solution to two-dimensional Korteweg-de Vries-Burgers equation. (English) Zbl 0771.35059
Summary: By applying a special solution of square Hopf-Cole type to an ordinary differential equation, we propose a bounded travelling wave solution u(x,y,t)=v(ξ)=v(kx+ly-ωt) to the two-dimensional Korteweg-de Vries-Burgers equation is monotonic and possesses an inflection point with respect to ξ.

MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35C05Solutions of PDE in closed form