Abstract
We study a two-dimensional integrable generalization of the Kaup-Kupershmidt equation, which arises in various problems in mathematical physics. Exact solutions are obtained using the Lie symmetry method in conjunction with the extended tanh method and the extended Jacobi elliptic function method. In addition to exact solutions we also present conservation laws which are derived using the multiplier approach.
Highlights
The theory of nonlinear evolution equations (NLEEs) has made a substantial progress in the last few decades
In addition to exact solutions we present conservation laws which are derived using the multiplier approach
Exact solutions of NLEEs arising in fluid dynamics, continuum mechanics, and general relativity are of considerable importance for the light they shed into extreme cases which are not susceptible to numerical treatments
Summary
The theory of nonlinear evolution equations (NLEEs) has made a substantial progress in the last few decades. We will use Lie symmetry method along with the extended tanh method and the extended Jacobi elliptic function method to obtain new exact solutions of (1). The extended tanh method and extended Jacobi elliptic function method are applied to the system of ordinary differential equations and as a result we obtain the exact explicit solutions of our two-dimensional integrable generalization of the Kaup-Kupershmidt equation (1). One of the main reasons for calculating symmetries of a differential equation is to use them for obtaining symmetry reductions and finding exact solutions. It is well known fact that the reduction of a partial differential equation with respect to r-dimensional (solvable) subalgebra of its Lie symmetry algebra leads to reducing the number of independent variables by r. A profile of solutions (17), (19) is given in Figures 2 and 3
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
