Abstract
In this work, we study the completely integrable sixth-order nonlinear Ramani equation. By applying the Lie symmetry analysis technique, the Lie point symmetries and the optimal system of one-dimensional sub-algebras of the equation are derived. The optimal system is further used to derive the symmetry reductions and exact solutions. In conjunction with the Riccati Bernoulli sub-ODE (RBSO), we construct the travelling wave solutions of the equation by solving the ordinary differential equations (ODEs) obtained from the symmetry reduction. We show that the equation is nonlinearly self-adjoint and construct the conservation laws (CL) associated with the Lie symmetries by invoking the conservation theorem due to Ibragimov. Some figures are shown to show the physical interpretations of the acquired results.
Highlights
It is well-known that the majority of real-world physical phenomena are modeled by mathematical equations, especially partial differential equations (PDEs)
In order to understand the understanding of such physical phenomena, it is vital to look for the exact solutions of the PDEs
conservation laws (CL) are important in determining the integrability of PDEs [2]
Summary
It is well-known that the majority of real-world physical phenomena are modeled by mathematical equations, especially partial differential equations (PDEs). In reference [14], the Lax. Symmetry 2018, 10, 341 pairs and Bäcklund transformation were applied to study the equation. The invariant solutions are derived by solving the ordinary differential equations (ODEs) obtained from the symmetry reduction process using the Riccati Bernoulli sub-ODE (RBSO) [19]. In this part, we construct the vector fields of Equation (1).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
