Physical Structures For Three Types Of Nonlinear Boussinesq Equations

Three types of nonlinear Boussinesq equations are investigeted inthis paper. The exact travelling wave solutions of the equations are obtained byusing the sine-cosine ansatz and a technique which is based on the reduction oforder for solving di?erential equation.More specifically, in chapters 2 and 3, we use the sine-cosine ansatz to studythe following two kinds of Boussinesq equations.andThe complex solutions for(0-3)and the compactons, solitary patterns, soli-tons and periodic solutions for equations (0-4) are obtained. It is shown thatthe physical structures of the solutions are directly dependent of the main coef-ficients presented in the Boussinesq system.In chapter 4, by developing a mathematical technique di?erent from thosein [7–9], we examine the Boussinesq-type of equations with positive exponentsand the Boussinesq-type of equations with negative exponentswhere a, b = 0 are constants.The compactons, solitary patterns, solitons and periodic solutions for equa-tions (0-5)and(0-6) are obtained. It is pointed out that our results includeWazwaz's results presented in [7] as special cases. Similar to Wazwaz's resultsin [7], it is shown that the di?erent physical structures of the solutions such as compactons, solitons, solitary patterns and periodic solutions, depend on theratio a/b and exponent n.