A complex solution to (3+1)-dimensional kdv and (3+1)-dimensional kdv-burger equations in bubbly liquid

Abstract

In this paper, we use secant hyperbolic ansatz with tanh-coth method, combined with Riccati equation to derive complex travelling wave solutions to the (3+1)-dimensional Korteweg-de-Vries (KdV) and (3+1)-dimensional KdV-Burgers equations. Both the complex solitary and periodic solutions for (3+1)-dimensional KdV equation were obtained. For the (3+1)-dimensional KdVB equation, the real part is the sum of the shock wave solution of a (3+1) dimensional Burgers equation and the solitary wave solution of a (3+1)-dimensional KdV equation, while the imaginary part is the product of a shock wave solution of (3+1)-dimensional Burgers equation with a solitary wave solutions of (3+1)-dimensional KdV equation.