Soliton Solutions and Conservation Laws for an Inhomogeneous Fourth-Order Nonlinear Schrödinger Equation

Abstract

In this paper, we investigate an inhomogeneous fourth-order nonlinear Schrödinger (NLS) equation, generated by deforming the inhomogeneous Heisenberg ferromagnetic spin system through the space curve formalism and using the prolongation structure theory. Via the introduction of the auxiliary function, the bilinear form, one-soliton and two-soliton solutions for the inhomogeneous fourth-order NLS equation are obtained. Infinitely many conservation laws for the inhomogeneous fourth-order NLS equation are derived on the basis of the Ablowitz–Kaup–Newell–Segur system. Propagation and interactions of solitons are investigated analytically and graphically. The effect of the parameters \({{\mu }_{1}}\), \({{\mu }_{2}}\), \({{\nu }_{1}}\) and \({{\nu }_{2}}\) on the soliton velocity are presented. Through the asymptotic analysis, we have proved that the interaction of two solitons is not elastic.