Advanced Mathematical Models & Applications

The present study aims to propose and thoroughly investigate the Kawahara equation with dual power-law nonlinearities, which is a fifth-order nonlinear partial differential equations that models complex wave phenomena in various scientific disciplines, including fluid dynamics, plasma physics, and nonlinear acoustics. The study employs Lie group analysis in search for exact solutions of the equation. Through this investigation, the Lie point symmetries admitted by the Kawahara equation are identified, exhibiting two translation symmetries. The combination of these symmetries allows the construction of travelling wave solutions. By using these two symmetries, the original equation is reduced to a nonlinear ordinary differential equation (NODE). This NODE is then solved using special analytical methods, including Kudryashov’s method and the extended Jacobi elliptic function expansion method, both of which are well-suited for obtaining exact and periodic solutions. To illustrate the physical behaviour of the obtained solutions, 3D, 2D, and density plots are presented. Finally, conserved vectors of the equation are derived using the multiplier technique and Noether’s theorem.