Abstract. Using the reductive perturbation technique, the nonplanar cylindrical and spherical modified Burgers' equations are derived for dust ion acoustic waves in an unmagnetized dusty plasma, whose constituents are adiabatic ion fluid, Boltzmann electrons and negatively charged static dust particles. The solution of modified Burgers' equations in nonplanar geometry is numerically analyzed. The properties of dust ion acoustic waves in nonplanar cylindrical and spherical geometry are investigated. It has been found that the nonplanar geometry effects have a very significant role in the formation of shock waves. We have also reduced the modified Burgers' equation to an ordinary nonlinear differential equation using the Lie algebraic method. The numerical solution of these equations is given for two values of η₀, the viscosity parameter.

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