New Solitary Solutions Of Full Nonlinear Evolution Equations

In this paper, the major contents conclude: Introduce the concept of nonlinear intensity, we study exact solutions for full nonlinear evolution equations(compacton solutions, peakon solutions, kink solutions, bell-shaped solitary solutions) and its Backlund transformations. Then consider their Hamilton structure and some conservation laws. At last we prove that linear stabilityof all multi-compacton solutions.In the third chapter, we introduce the fifth-order K(m,n,1) equation with nonlinear dispersion, and obtain compacton solutions by ansatzs method and adomian decomposition method, and we further study it in higher dimensions. Using homogenous balance(HB) method, we obtain a Backlund transformation of K(2,2,1) equation and obtain some solitary solutions in the equation. We give a similar fifth-order equation which derived from Lagrangian, and obtain Hamilton structure and some conservation laws. At last we prove that linear stability.In the forth chapter, we introduce the fully nonlinear generalized Camassa-Holm equation and by using direct ansatzs, we obtain compacton solutions. We use the direct reduction method(CK method) to all the reductions, and the result of reductions gives rise to abundant solutions: compacton solutions, peakon solutions, kink solutions, bell-shaped solitary solutions.In the fifth chapter, We research nonlinear Schrodinger equation. Obtain abundant solitary solutions, particularly obtain displace compacton solutions when p<0. We also get compacton solutions of higher dimension nonlinear Schrodinger equation. And also we compare the solutions in arbitrary dimensions, and the relation between solutions with parameters.In the sixth chapter, we study full nonlinear sine-Gordon equation SG(m,n,p). Obtain kink solutions and a new type of peakon solutions in a direct method. And obtain peakon solutions and a new type of compacton solutions for approximate SG(m,n,p) equation. At last, we study full nonlinear sine-Gordon equation in high demension.In the seventh chapter, we study generalized Ostrovskyequation, and use direct ansatzs, obtain compacton solutions. Then study some conservation laws and its linear stability.