For 0 < α 1, N ⩾ 2 and with initial data ‖ u H + = ε, sufficiently small, we show that the existence time for solutions of fractional BBM equation ∂ t x | D 0, can be extended from hyperbolic 1 ε to . proof use a quasilinear modified energy method, based on normal form transformation as in Hunter, Ifrim, Tataru, Wong (Proc. Am. Math. Soc., 143(8) (2015) 3407–3412).

The regularized long-wave or BBM equation ut + ux + uux − uxxt = 0 was derived as a model for the unidirectional propagation of long-crested, surface water waves. It arises in other contexts as well, and is generally understood as an alternative to the Korteweg-de Vries equation. Considered here is the initial-value problem wherein u is specified everywhere at a given time t = 0, say, and inqui...

Geometric integrators are presented for a class of nonlinear dispersive equations which includes the Camassa-Holm equation, the BBM equation and the hyperelasticrod wave equation. One group of schemes is designed to preserve a global property of the equations: the conservation of energy; while the other one preserves a more local feature of the equations: the multi-symplecticity.

In this paper, a numerical solution of nonlinear partial differential equation, Benjamin-Bona-Mahony (BBM) and Cahn-Hilliard equation is presented by using Adomain Decomposition Method (ADM) and Variational Iteration Method (VIM). The results reveal that the two methods are very effective, simple and very close to the exact solution.

In this paper, we investigate the first integral method for solving the generalized Benjamin-BonaMahony (BBM) equation. This idea can obtain some exact solutions of this equations based on the theory of Commutative algebra.

In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...

In this paper, we consider the following linear Korteweg–de Vries–Benjamin Bona Mahony (KdV-BBM) equation on a finite interval.$ \left\{ \begin{array}{ll} u_t - a^2u_{xxt} + u_x u_{xxx} = 0, & (x, t)\in(0, L)\times (0, \infty), \\ u(0, t) u(L, u_x(L, &t\in u(x, 0) u_0(x), x \in L). \end{array} \right. $We show well-posedness by semigroup theory. A set of critical length $ \mathcal{L} is...