Lax pair, Darboux transformation, Weierstrass–Jacobi elliptic and generalized breathers along with soliton solutions for Benjamin–Bona–Mahony equation

Abstract

This paper studies the Lax pair (LP) of the [Formula: see text]-dimensional Benjamin–Bona–Mahony equation (BBBE). Based on the LP, initial solution and Darboux transformation (DT), the analytic one-soliton solution will also be obtained for BBBE. This paper contains a bunch of soliton solutions together with bright, dark, periodic, kink, rational, Weierstrass elliptic and Jacobi elliptic solutions for governing model through the newly developed sub-ODE method. The BBBE has a wide range of applications in modeling long surface gravity waves of small amplitude. In addition, we will evaluate generalized breathers, Akhmediev breathers and standard rogue wave solutions for stated model via appropriate ansatz schemes.