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- W1854239734 abstract "where u(x, t) represents the fluid velocity in the horizontal direction x, α is a positive constant, β ∈ R and g(u) is a C 2 -smooth nonlinear function. In the physical sense, equation (1) with the dissipative term −αuxx is proposed if the good predictive power is desired, such problem arises in the phenomena for both the bore propagation and the water waves. Benjamin-Bona-Mahony-Burgers equations have a special kind of solutions: the solitary waves and the property of existence of a finite number of quantities (with physical interpretation) conserved by the solutions. The temporal decay rates of the solution of (1) and its special cases are studied in a number of works. [1] studied the large-time behavior of the global solutions to the Cauchy problem for (1). [2] used the decomposition method for the numerical solution subject to appropriate initial condition of (1) to consider solitary-wave solutions of generalized BBMB equations. [3] applied variational iteration method and homotopy perturbation methods to derive approximate explicit solutions for a special form of (1). [4] used hompotopy analysis method to BBMB equations. [5] concerned (1) for special case α =1 and β =0 , in this special case we have the long-wave equation ut − uxxt − uxx +( g(u))x =0 . (2)" @default.
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- W1854239734 date "2010-01-22" @default.
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- W1854239734 title "Exact Three-wave Solutions for High Nonlinear Form of Benjamin-Bona-Mahony-Burgers Equations" @default.
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