New and more exact traveling wave solutions to integrable (2+1)-dimensional Maccari system

In this article, new and general exact traveling wave solutions including soliton-like solutions, triangular-type solutions, single and combined nondegenerate Jacobi elliptic wave function-like solutions, doubly periodic-like solutions are obtained for integrable (2+1)-dimensional Maccari system. This system is frequently introduced to define the motion of the isolated waves, localized in a very small part of space, in many fields such as quantum field theory, hydrodynamics, in plasma physics to describe the behavior of the sonic Langmuir solitons, and also in nonlinear optics. Based on the generalized elliptic equation, an algebraic method is used to construct a series of exact solutions. Being concise and straightforward, the calculations demonstrate the effectiveness and convenience of the method for solving other nonlinear partial differential equations.