The study titled “Undular bores in the (3+1) dimensional mK equation” was published in Journal: Physics Letters A by ITU Mathematics Engineering faculty members Prof. Dr. Semra Ahmetolan and Assoc. Prof. Dr. Ali Demirci, and the Phd student Neşe Özdemir, MsC.

Undular bores (UBs), which are also called dispersive shock waves (DSWs), are nonlinear modulated wave trains and can be observed in many research fields such as fluids, plasma physics and optics. In this study, UB solutions in the (3+1) dimensional modified Kadomtsev-Petviashvili (mKP) equation for step type initial condition along a paraboloid type wavefront are found. Then, using a suitable solution form for the (3+1) dimensional mKP equation, it is reduced to the (1+1) dimensional focusing spherical mKdV (smKdV) and defocusing spherical mKdV (smKdV(d)) equations. Next, the Whitham modulation equations of the smKdV and smKdV(d) equations are found in terms of Riemann variables. Numerical solutions of the derived modulation equations are obtained. Also, an error analysis is performed for direct numerical solutions of both smKdV and smKdV(d).