The present study discloses the evaluation of second-order elastic constants of wurtzite boron nitride(w-BN) at room temperature and at different pressures using the many-body interaction potential model approach. Orientation- and pressure-dependent ultrasonic velocity, thermal relaxation time and other related thermophysical parameters (Debye temperature, Debye average velocity, specific heat and thermal energy density) are also calculated using the evaluated second-order elastic constants. The orientation-dependent thermal relaxation time of w-BN is predominantly affected by the Debye average velocity and is indirectly governed by second-order elastic constants. Thermal relaxation time of w-BN is found to decrease with pressure. Calculated elastic and ultrasonic properties of w-BN are compared with the properties of other wurtzite structured materials for a complete analysis and characterisation of the material.

In this work, Lie symmetry analysis and one-dimensional optimal system for Pavlov equation are presented. All the possible vector fields, their commutative and adjoint relations are carried out under invariance property of Lie group theory. On the basis of optimal system, similarity reductions of Pavlov equation are obtained. A repeated process of similarity reductions transforms the Pavlov equation into ordinary differential equations, which generate invariant solutions. The obtained invariant solutions are supplemented by numerical simulation toanalyse the physical behaviour. Thus, their parabolic, multisoliton, nonlinear, kink and antikink wave profiles are traced in results and discussions sections.