New closed-form soliton solutions for the tzitzeica dodd bullough equation arising nonlinear optics via three distinct re-liable approaches

Abstract

Tzitzeica Dodd Bullough (TDB) equation appears in the field of quantum field theory and nonlinear optics. In this article, we extracted abundant new soliton solutions with free choice of arbitrary parameters to the Tzitzeica-Dodd-Bullough (TDB) equation through the three separate methods such as the enhanced -expansion method, the improved -expansion method and the -expansion method by means of the wave transformation and the Painleve property. In these schemes, we formally derived some new closed form soliton solutions of the TDB equation through with symbolic computation package Maple. Soliton solutions are expressed by hyperbolic function, trigonometric function and rational function. The attained solutions are verified by symbolic computation software Maple 17. The attained solutions can be demonstrated by two-dimensional (2D) and three-dimensional (3D) graphs. Finally, it can be concluded that the adopted methods are very effective and well-suited to find new closed-form soliton solutions to the other nonlinear evaluation equations (NLEEs) with integer or fractional order.