Solitary wave solutions for modified forms of Degasperis–Procesi and Camassa–Holm equations

Solitary wave solutions for modified forms of Degasperis–Procesi and Camassa–Holm equations are developed. Unlike the standard Degasperis–Procesi and Camassa–Holm equations, where multi-peakon solutions arise, the modification caused a change in the characteristic of these peakon solutions and changed it to bell-shaped solitons. The tanh method and the sine–cosine method are used to achieve this goal.