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Abstract
The work on traveling wave solutions of the nonlinear beam equation and their stability and interaction properties is continued. The equation is a partial differential equation of fourth order in space and second order in time. While this equation has been previously studied in one space dimension, this is the first time a multidimensional case is considered. A proof of existence of traveling wave solutions in two and three space dimensions for a certain class of nonlinearities is presented using mountain pass theory. A description of the Mountain Pass Algorithm is given. The algorithm is then employed to obtain the traveling wave solutions numerically in two space dimensions. A single and double-pulse waves are found for a range of values of the wave speed. A parallel version of an explicit finite difference scheme is used to study stability properties of the waves. Fission of the double-pulse wave into two single-pulse waves is observed. When two single-pulse waves travel in opposite directions and collide, they emerge from the collision almost unchanged.