Utilizing two methods to discover novel travelling wave solutions for the \((2+1)\)-dimensional Chiral nonlinear Schrödinger equation

In this article, the extended fan method and the positive quadratic function technique are used to solve the \((2+1)\) $(2+1)$ -dimensional Chiral nonlinear Schrödinger equation. Several new outcomes are obtained. Several new results are obtained. We can offer soliton-type solutions, triangular-type solutions, simple and combined solutions using Jacobi’s elliptic functions. Using suitable parameters, some graphics are given to observe the evolution of these analytical solutions. Many other nonlinear differential equations can benefit from using the methods proposed in this work.