Exact solutions for some nonlinear evolution equations which describe pseudo-spherical surfaces

For some nonlinear evolution equations which describe pseudo-spherical surfaces two new exact solution classes are generated from known solutions: either the seed solution is constant or a traveling wave. Exact traveling wave and solitary wave solutions for Burgers’ equation and also for a fifth-order evolution equation containing the fifth-order Korteweg–de Vries equation and also the Sawada–Kotera equation, are obtained by using an improved sine–cosine method and the Wuʹs elimination method. We also apply Bäcklund transformations to these solutions and generate new soliton solution classes.