Abstract
The Jacobi elliptic function method is applied to solve the generalized Benjamin-Bona-Mahony equation (BBM). Periodic and soliton solutions are formally derived in a general form. Some particular cases are considered. A power series method is also applied in some particular cases. Some solutions are expressed in terms of the Weierstrass elliptic function.
Highlights
The regularized long-wave (RLW) equation is a famous nonlinear wave equation which gives the phenomena of dispersion and weak nonlinearity, including magneto hydrodynamic wave in plasma, phonon packets in nonlinear crystals, and nonlinear transverse waves in shallow water or in ion acoustic
This equation is called the Benjamin-Bona-Mahony equation (BBM) (BenjaminBona-Mahony) equation and reads ut + uux + ux − μuxxt = 0: ð1Þ. It describes approximately the unidirectional propagation of long waves in certain nonlinear dispersive systems, and it was proposed by Benjamin et al in 1972 [1] as a more satisfactory model than the KdV equation [2]: ut + uux + uxxx = 0: ð2Þ
It is easy to see that Equation (1) can be derived from the equal width equation [3]: ut + uux − μuxxt = 0, ð3Þ
Summary
The regularized long-wave (RLW) equation is a famous nonlinear wave equation which gives the phenomena of dispersion and weak nonlinearity, including magneto hydrodynamic wave in plasma, phonon packets in nonlinear crystals, and nonlinear transverse waves in shallow water or in ion acoustic. This equation is called the BBM (BenjaminBona-Mahony) equation and reads ut + uux + ux − μuxxt = 0: ð1Þ.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call