Abstract
This study deals with symmetry reductions and invariant solutions of (2+1)-dimensional dissipative Zabolotskaya–Khokhlov equation. The equation governs the diffraction of sound beam propagation and describes nonlinear effects in stratified media with dissipation. The possible infinitesimal generators and commutative relation are obtained by means of the similarity transformations method. The method is based on invariance property of Lie groups, which results into the reduction in independent variables by one. Thus, twice reductions of Zabolotskaya–Khokhlov equation provide overdetermined equations, which lead to the invariant solutions under some limiting conditions. The obtained solutions are significant to explain diverse physical structures depending upon existing arbitrary functions and constants. In order to get precise insights, the numerical simulation is performed to the obtained solutions. Eventually, kink wave, parabolic, soliton and stationary profiles of the solutions are obtained.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
