The modified auxiliary equation (MAE) approach and the generalized projective Riccati equation (GPRE) method are used to solve the Zoomeron problem in this study. Different types of exact traveling wave solutions are achieved, including solitary wave, periodic wave, bright, dark peakon, and kink-type wave solutions. Earned results are given as hyperbolic and trigonometric functions. Moreover, the dynamical features of obtained results are demonstrated through interesting plots.

This article investigates the fractional Peyrard-Bishop DNA model. The construction of soliton solutions have been successfully obtained by utilizing two versatile analytical methods, namely, the Jacobi elliptic function method and the tanh-coth method. Furthermore, the Painlev´e test (P-test) has been employed on the proposed model for investigating integrability. The proposed model is proved to be integrable. Some of the obtained solutions have been examined graphically to study the dynamical behavior.

The aim of the present paper is to extract the exact traveling wave solutions of the chiral nonlinear Schr\”{o}dinger’s equation (cNLSE). The $(\frac{G’}{G^{2}})-$expansion method and the first integral method along with symbolic computation package has been exerted to celebrate the exact solutions. As a consequence, the obtained solutions can be categorized into trigonometric, hyperbolic and rational with some free parameters of the problem studied. In addition, these types of the solutions lead to understand the physical phenomena of the problem such as solitary, periodic, complex function, singular optical solitons and dark-singular combo solitons.

In this manuscript, some novel exact traveling wave solutions are constructed for $(2+1)$-dimensional Boiti-Leon-Manna-Pempinelli(BLMP) equation. The analytical techniques, namely extended rational sine-cosine method and extended rational sinh-cosh method are utilized for constructing the new solitary wave solutions of BLMP equation. The proposed techniques provides different types of solutions which are expressed in terms of singular periodic wave, solitary waves, bright solitons, dark solitons, periodic wave and kink wave solutions with specific values of parameters.