title: An ansatz for solving nonlinear partial differential equations in mathematical physics.
abstract: In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.
authors.affiliation: Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh.
authors.forename: M Ali
authors.identifier: 0000-0001-5688-6259
authors.initials: MA
authors.lastname: Akbar
authors.affiliation: School of Mathematical Sciences, Universiti Sains Malaysia, George Town, Malaysia.
authors.forename: Norhashidah Hj Mohd
authors.initials: NH
authors.lastname: Ali
keywords: (1+1)-dimensional modified Benjamin–Bona–Mahony equation; Ansatz method; NLPDEs; Traveling wave solutions