The Generalized Regularized Long Wave Equation
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چکیده
where and are positive constants, was first proposed by Peregrine [74] for modeling the propagation of unidirectional weakly nonlinear and weakly dispersive water waves. Later on Benjamine et al. [9] proposed the use of the RLW equation as a preferred alternative to the more classical Korteweg de Vries (KdV) equation to model a large class of physical phenomena. These authors showed that RLW equation is better posed than the KdV-equation. The RLW equation is one of the model partial differential equation of the nonlinear dispersive waves which has many applications in many areas e.g. ion-acoustic waves in plasma, megnetohydrodynamic waves in plasma, longitudinal dispersive waves in elastic rods, pressure waves in liquid-gas bubble mixtures and rotating flow down a tube. The solutions of this equation are kinds of solitary waves named solitons, whose shapes are not affected by collision. Indeed, the RLW equation is a special case of the generalized regularized long wave (GRLW) equation given by 0 ) 1 ( xxt x p x t u u u p p u u , (7.1.2)
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