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In this thesis, we summarize our recent contribution to the pattern dynamics in the Hamiltonian system. Our new results are: 1.A very useful method to study pattern dynamics in the Hamiltonian system has been suggested, so long as a few representative manifolds are investigated one can understand the dynamical properties of such complicated sustem. 2.The pattern formation and competition as well as the spatio-temporal chaos in the cubic and cubic-quintic Nonlinear Schrodinger Equation have been investigated. We found that Hamiltonian perturbation, but not external force and dissipation, can cause homoclinic crossings that symbol chaotic motion in an extended spatial system. The routes to such phenomena are discussed by using the method of representative manifolds and explained in the terms of oscllators overlapping. The numerical calculations of correlation length are also carried out. 3.Some cutoff models for studying the low dimensional behaviors of Nonlinear Schrodinger Equation in modulation instability are also suggested. We found that only in the neighbour of the threshold value of unstable warenumber, the low dimensional behaviors are true. Away from the threshold value, the higher modes will not be ignorable.