A Laguerre-Galerkin method is proposed and analyzed for the Burgers equation and Benjamin-Bona-Mahony (BBM) equation on a semiinfinite interval. By reformulating these equations with suitable functional transforms, it is shown that the Laguerre-Galerkin approximations are convergent on a semi-infinite interval with spectral accuracy. An efficient and accurate algorithm based on the Laguerre-Gal...

The paper concerns capillary-gravity surface waves propagating on a two-dimensional incompressible and inviscid fluid with or without an obstacle placed at flat horizontal bottom. Formally second-order correct model equations, analogous to the first-order KdV equation, are derived under classical assumptions of long wavelength small amplitude waves. equations fifth-order type where bottom intro...

The BBM or Regularized Long Wave Equation is shown to possess only three non-trivial independent conservation laws. In order to prove this result, a new theory of Euler-type operators in the formal calculus of variations will be developed in detail.

An auxiliary equation technique is applied to investigate a generalized Benjamin-Bona-Mahony equation with variable coefficients. Many exact traveling wave solutions are obtained which include algebraic solutions, solitons, solitary wave solutions and trigonometric solutions. Mathematics Subject Classification: 35Q53, 35B35

Dietary proteins are recognized by the gastrointestinal tract to display physiological functions, however, the sensory mechanism of the intestinal mucosa is not known. We examined binding properties between the rat small intestinal brush-border membrane (BBM) and proteins by using a surface plasmon resonance biosensor. BBM and solubilized BBM prepared from the rat jejunum bound to casein immobi...

In this paper, a simple, robust, fast and effective method based on the conserved quantities is developed to approximate analyse shape, structure interaction characters of solitary waves described by Benjamin–Bona–Mahony (BBM) equation. Due invariant character quantities, there no need solve related complex nonlinear partial differential BBM equation simulate interactions between at most mergin...

We use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the generalized KP-BBM equation. A number of explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain periodic wave solutions, kink wave solutions, unbounded wave solutions, blow-up wave sol...

Abstract We show that the Benjamin–Bona–Mahony (BBM) equation admits stable travelling wave solutions representing a sharp transition from constant state to periodic train. The is determined by parameters of train: length, amplitude and phase velocity, satisfies both generalized Rankine–Hugoniot conditions for exact BBM its averaged counterpart. Such shock-like structures exist if velocity trai...