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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 \(u(x,y,t)=v(\xi)=v(kx+ly-\omega t)\) to the two-dimensional Korteweg-de Vries-Burgers equation is monotonic and possesses an inflection point with respect to \(\xi\).

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C05 Solutions to PDEs in closed form
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