The research paper ”Benney–Roskes/Zakharov–Rubenchik System: Lie Symmetries And Exact Solutions” based on the studies conducted by ITU Department of Mathematics Engineering members Assoc. Prof. Dr. Cihangir Özemir and Res. Assis. Şeyma Gönül was published in The European Physical Journal Plus.
In this study, they investigated the system of Benney-Roskes/Zakharov-Rubenchik PDEs in (2+1)-dimensional case, from a group-theoretical point of view. They included the wave models Davey-Stewartson system and Zakharov systems as limiting cases. They found that the symmetry algebra of the (2+1) Benney-Roskes/Zakharov-Rubenchik system is an infinite-dimensional Lie algebra. By a traveling wave ansatz, they obtained several exact solutions in terms of trigonometric, hyperbolic and elliptic functions. Besides the periodic exact solutions, to their knowledge, they have obtained the result of a line soliton for the first time in the literature. It is believed that these results will serve as a source for future numerical and qualitative studies on this system.