Conservation laws and new exact solutions to the maccari’s modulation equations

Abstract

Abstract In this work the (2+1) dimensional integrable Maccari system is studied. An effective algorithmic method—the multiplier approach for finding the conservation laws of system of partial differential equations is discussed and used to find the conservation laws for this system. Infinite number of conserved vectors are found which strongly support the integrability aspects of the Maccari system. Also new exact solution for this system is derived by using the extended homogeneous balance method. The obtained solutions are plotted and they show bright and dark soliton nature.