An analytic approach to constructing Backlund transformations and exact solutions to nonlinear wave equations in non-polynomial form

Backlund transformation (BT) is an intrinsic property of nonlinear integrable system. Generally, it is an interesting and challenging work to investigate BT of a nonlinear system, especially for the non-polynomial form. In this paper, we introduce an analytic method for constructing BTs of the generalized nonlinear wave equations (NLWEs) of the form u(tt) = au(xx) + h(u). The BTs with arbitrary parameters are provided explicitly, so the integrability of the equation is verified accordingly. Then, the nonlinear superposition formulas (NSFs) of the NLWEs are given in terms of such BTs, and the infinite number of exact explicit solutions to the equations are obtained based on the BTs and the NSFs. Furthermore, the BTs of the other types of NLWEs of the form u(xt) = h(u) can be provided directly by the variable transformation method. (C) 2019 The Authors. Published by Elsevier B.V.