Nonlinear Science and Complexity (Transactions of Nonlinear by Albert C J Luo, Liming Dai, Hamid R Hamidzadeh

By Albert C J Luo, Liming Dai, Hamid R Hamidzadeh

This quantity presents worthwhile instruments in Lie staff research to resolve nonlinear partial differential equations. lots of very important matters in nonlinear wave dynamics and nonlinear fluid mechanics are offered: Homotopy ideas are used to procure analytical strategies; primary difficulties and theories in vintage and quantum dynamical structures are mentioned; and various attention-grabbing effects approximately dynamics and vibration in sensor and shrewdpermanent platforms are provided. period computation and nonlinear modeling in dynamics and keep watch over also are in brief integrated.

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Extra resources for Nonlinear Science and Complexity (Transactions of Nonlinear Science and Complexity)

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2155, then in system (3), there is a stable cycle of period 40, which corresponds to the cycle 5*23 in the Sharkovskii order. 348. The generation of the last cycle implies the generation of a stable cycle of period 3 in some two-dimensional plane transversal to the original cycle. 0, a stable cycle of period 3. All generated cycles undergo their own cascades of Feigenbaum period doubling bifurcations. It is important to note that, in the three-dimensional phase space (x, y,z) of system (3), for some parameter values, there can simultaneously exist several distinct stable cycles with their attraction domains.

The crosses represent the numerical results of the eigenvalue problem. S. Stability of specific solitary waves Here we investigate the stability of specific solitary waves. The solitary wave solutions are numerically calculated using the method described in Turner & Vanden-Broeck (1988). According to the previous studies (Funakoshi & Oikawa 1986; Amick & Turner 1986; Turner & Vanden-Broeck 1988), there are two types of interfacial solitary waves depending on the parameters p and D. One is of elevation type (p D2).

SO, dy AxAy , (24) J—co 3 Asymptotic analysis Proposition Suppose that the solitary wave solutions (0, dv where AM AQ.

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