The quasi-periodic Cauchy problem for the generalized Benjamin-Bona-Mahony equation on the real line

This paper studies the existence and uniqueness problem for the generalized Benjamin-Bona-Mahony (gBBM) equation with quasi-periodic initial data on the real line. We obtain an existence and uniqueness result in the classical sense with arbitrary time horizon under the assumption of polynomially decaying initial Fourier data using the combinatorial analysis method developed in earlier papers by Christ [6], Damanik-Goldstein [11], and the present authors [12]. Our result is valid for exponentially decaying initial Fourier data and hence can be viewed as a Cauchy-Kovalevskaya theorem in the space variable for the gBBM equation with quasi-periodic initial data. (c) 2023 Elsevier Inc. All rights reserved.