Hopf-Cole Transformation with Effect of the Dissipation Coefficient on Nonlinearity in the Benjamin-Bona-Mahony (BBM) Generalized Pseudo-Parabolic Equation

R. Gilles Bokolo

Abstract: In this paper, we consider the general form of the Benjamin-Bona-Mahony's pseudo-parabolic nonlinear equation (BBM) in which we use the Hopf-Cole transformation [10]. We also set up a conjecture to get rid of several terms throughout our development. Finally, we present a comparative analysis of solutions found either by the aforementioned transform or by the functional variable method formulated by A. Zerarka [11]- [12]. Hence, we show that the result obtained by the approach of Hopf- Cole transformation has some significant features.

Keywords: pseudo-parabolic nonlinear equation, generalized Benjamin-Bona-Mahony equation BBM, functional variable method, Hopf-Cole transformation