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.

在本文中，我们旨在研究（1+2）维手征非线性薛定谔方程。采用复数变换将方程转换为实部和虚部。变分原理是由半逆方法开发的。然后我们有史以来第一次扩展了他的变分方法来构造新的丰富解，包括亮孤子、亮暗孤子、类亮孤子、扭亮孤子和周期解。使用扩展的He变分法，我们可以通过变分原理降低所研究方程的阶数，使方程更简单，从而得到平稳条件下的最优解。最后，我们用一个例子通过3-D图来验证扩展He变分方法的有效性和可靠性。