New perturbed conformable Boussinesq-like equation: Soliton and other solutions

In recent years, finding exact solutions to nonlinear differential equations has become a fascinating study topic. In the present study, using the modified Kudryashov method and the improved generalized Riccati equation mapping method in the conformable sense, we acquired the exact soliton-type solutions for the new time-fractional perturbed Boussinesq-like equation. This equation has been successfully obtained by the use of asymptotic methods on the defocusing Camassa–Holm nonlinear Schrödinger equation. We obtain the exponential, trigonometric, hyperbolic, and rational type solutions comprising dark solitons, kink solitons, bisymmetry solitons, singular solitons, combined complex solitons, and periodic solutions. These solutions are of great importance in various fields of applied sciences, coastal, and ocean engineering. Furthermore, all acquired solutions have been validated by putting them back into the original equation with the help of the Mathematica package software.