Breather waves, analytical solutions and conservation laws using Lie–Bäcklund symmetries to the (2+1)-dimensional Chaffee–Infante equation

The ($2+1$)-dimensional Chaffee–Infante has a wide range of applications in science and engineering, including nonlinear fiber optics, electromagnetic field waves, signal processing through optical fibers, plasma physics, coastal engineering, fluid dynamics and is particularly useful for modeling ion-acoustic waves in plasma and sound waves. In this paper, this equation is investigated and analyzed using two effective schemes. The well-known tanh-coth and sine-cosine function schemes are employed to establish analytical solutions for the equation under consideration. The breather wave solutions are derived using the Cole–Hopf transformation. In addition, by means of new conservation theorem, we construct conservation laws (CLs) for the governing equation by means of Lie–Bäcklund symmetries. The novel characteristics for the ($2+1$)-dimensional Chaffee–Infante equation obtained in this work can be of great importance in nonlinear sciences and ocean engineering.