On similarity solutions of Zabolotskaya–Khokhlov equation

The new closed form solutions of the (2+12+1)-dimensional Zabolotskaya–Khokhlov equation are constructed by using the similarity transformations method via Lie group theory. The Zabolotskaya–Khokhlov equation has been reduced into a new partial differential equation with smaller number of independent variables. Further using the similarity transformations method the new partial differential equation is reduced into an ordinary differential equation. The ordinary differential equation provides semi analytical solutions. Elastic behaviour of multisolitons and dromion annihilation of solutions are analyzed physically through their evolutional profiles.