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Showing 1 to 4 of 4 for “"homoclinic orbits"”.
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Forced Capillary-Gravity Waves in a 2D Rectangular Basin
… properties. A condition for the existence of homoclinic orbits connecting the trivial equilibrium is obtained. These results are confirmed by numerical experiments. The third part is based on the results in the second part. Here, one of the eigenfrequencies is chosen to be much larger than the …
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Investigation into the Local and Global Bifurcations of the Whirling Planar Pendulum
… of chaos are each associated with one of two homoclinic orbits in the system's phase portraits. The onset of each type of chaos is investigated through Melnikov's Method applied to the system's Hamiltonian, to find parameters at which the stable and unstable manifolds intersect transversely, …
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The nonlinear Schroedinger limit of the complex Ginzburg-Landau equation.
… power nonlinearity, it is proved that the NLS homoclinic orbits to rotating waves are destroyed by the CGL perturbation. Special attention is dedicated to the cubic case. For this nonlinearity, the NLS equation is a completely integrable Hamiltonian system and a much larger family of its …
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A Spatial Dynamic Approach to Three-Dimensional Gravity-Capillary Water Waves
… case (b,λ) â C₁. Then, from the existence of the homoclinic orbit connecting to the two-dimensional periodic solution (called generalized solitary wave) for the dominant system, it is obtained that such generalized solitary wave solution persists for the original system by using the perturbation …