Soliton solutions of Calogero-Degasperis-Fokas dynamical equation via modified mathematical methods

New solitary wave solutions of the Calogero-Degasperis-Fokas (CDF) equation via two modified methods called improved simple equation and modified F-expansion schemes are investigated. Numerous types of results are obtained in the form of hyperbolic functions, trigonometric functions and elliptic functions. Moreover, some of the derived solutions are illustrated as two-dimensional, three-dimensional and contour graphical images that were plotted with the assistance of computational software Mathematica, which gave useful knowledge to study the physical phenomena of the CDF model. The investigated solutions have fruitful advantages in mathematical physics.