Multiwave solutions of time-fractional (2 + 1)-dimensional Nizhnika€“Novikova€“Veselov equations

摘要

In this paper, we present a generalized unified method for finding multiwave solutions of the timefractional (2+1)-dimensional Nizhnika€“Novikova€“Veselov equations. The fractional derivatives are described in the modified Riemanna€“Liouville sense. The fractional complex transform has been suggested to convert fractional order differential equations with modified Riemanna€“Liouville derivatives into integer-order differential equations, and the reduced equations can be solved by symbolic computation. Multiauxiliary equations have been introduced in this method to obtain not only multisoliton solutions but also multiperiodic or multielliptic solutions. It is shown that the considered method is very effective and convenient for solving wide classes of nonlinear partial differential equations of fractional order.