Abstract
In this paper, we investigate the modified Boussinesq equation utt uxx # uxxxx 3(u 2 )xx + 3(u 2 ux)x = 0. Firstly, we give a property of the solutions of the equation, that is, if 1 + u(x,t) is a solution, so is 1 u(x,t). Secondly, by using the bifurcation method of dynamical sys- tems we obtain some explicit expressions of solutions for the equation, which include kink-shaped solutions, blow-up solutions, periodic blow-up solutions and solitary wave solutions. Some previous results are extended.
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