Abstract
Abstract Breaking dynamics of Riemann waves, has a profound impact on studying the dynamics of shock-breaking systems. Calogero– Bogoyavlenskii– Schiff (CBS) equation describes the interaction between Riemann propagating wave along y-axis with long propagating wave along x-axis. Two extensions of the CBS (2+1)-dimensional equation are investigated. Optimization of the commutative product for the nonlocal symmetry is constructed and two successive symmetry reductions reduced the equations to ordinary differential equations (ODEs). Hidden symmetries are used in the second reduction step. The singular manifold method (SMM) is then applied to the ordinary differential equations. This results in a Schwarzian derivative whose solution leads to Cuspon and Kink waves.
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