The Exact Solution Of The General Nonlinear Schrodinger Equation With Derivative And Ablowitz-ladik Lattice

The major contents in this paper consist of the exact solution of the General Nonlinear Schrodinger Equation with derivative and Ablowitz-Ladik Lattice are obtained.First, the General Nonlinear Schrodinger Equation with derivative is got by the Kaup-Newell spectral problem and Time development type, the Ablowitz-Ladik Lattice is obtain through the Ablowitz-Ladik spectral problem and Time development type. Secondly,The double Wronskian Solutions of the General Nonlinear Schrodinger Equation with Derivative are obtained through the Wronskian technique. By study, the consisteney of solutions were expressed through the Hirota method and the Wronskian technique, and its new forms of double Wronskian solutions are acquired by reduction. Finally, By using the Casoratian technique, we construct the double Casoratian Solutions of Ablowitz-Ladik Lattice. Soliton solutions and rational-like solutions are obtained from taking special cases in general solutions.The Second Chapter, taking into account the integrity of the paper, we describe some basic concepts and theorems related to the soliton theory, and list some of the results already achieved. In the third chapter, we give the double Wronskian Solutions of the General Nonlinear Schrodinger Equation with Derivative, then the coincidence of both solution is discussed. At last, the double Wronskian Solutions of the General Nonlinear Schrodinger Equation with Derivative is given by reducting. The fourth chapter, we give the double Casoratian Solutions of Ablowitz-Ladik Lattice, then the Soliton solutions and rational-like solutions are directly obtained from the general solutions.