Variational theory and new abundant solutions to the (1+2)-dimensional chiral nonlinear Schrödinger equation in optics

Abstract

In this paper, we aim to study the (1+2)-dimensional chiral nonlinear Schrödinger equation. A complex transform is adopted to convert the equation into the real and imaginary parts. The variational principle is developed by the Semi-inverse method. Then we, for the first time ever, extend He's variational method to construct the new abundant solutions, which include the bright soliton, bright-dark soliton, bright-like soliton, kinky bright soliton and the periodic solution. By using extended He's variational method, we can reduce the order of the studied equation through the variational principle, make the equation more simple and then obtain the optimal solutions by the stationary conditions. Finally, we use one example to verify the effectiveness and reliability of the extended He's variational method through the 3-D graphs. The obtained results in this work are helpful to be of significance to the study of traveling wave theory in physics.