Bäcklund transformation and conservation laws for the variable-coefficient N-coupled nonlinear Schrödinger equations with symbolic computation

Abstract

Considering the integrable properties for the coupled equations, the variable-coefficient Ncoupled nonlinear Schrödinger equations are under investigation analytically in this paper. Based on the Lax pair with the nonisospectral parameter, a Bäcklund transformation for such a coupled system denoting in the Γ functions is constructed with the one-solitonic solution given as the application sample. Furthermore, an infinite number of conservation laws are obtained using symbolic computation.

Blow-Up and Attractor of Solution for Problems of Nonlinear Schrodinger Equations

“…The non-linear Schrodinger equation is the basic equation in nonlinear science and widely applied in natural science such as the physics, chemistry, biology, communication and nonlinear optics etc. (See [1][2][3][4][5][6][7][8][9]) We study this equation to extend them are with important meaning (See [10][11][12]). …”