Variety Of Exact Wave Solutions Research Articles

Some new exact wave solutions and conservation laws of potential Korteweg–de Vries equation

The potential Korteweg–de Vries equation is investigated by using the sine–cosine method and generalized Kudryashov method. A variety of exact wave solutions that contain shock solutions, periodic solutions and solitons solutions are formally derived. Also, conservation laws of the equation is determined by using the multiplier approach. In addition, the restrictions on the physical parameters of obtained solutions are presented.

A variety of exact wave solutions with distinct physical structures for the Boussinesq system

The Boussinesq system is investigated by using the tanh method and the sine–cosine method. A variety of exact travelling wave solutions with compact and noncompact structures are formally obtained. The study shows that each method gives distinct solutions and one method complements the other.