In this talk, we will explore the advantages of using Jacobi Elliptic functions as expansion functions for solving various forms of patrial differential equations related to the Nonlinear Schrodinger equation [1]. The first key advantage is that such an approach gives us both solitary and traveling wave solutions by varying the parameter of the Jacobi function. Another key advantage is that the presence of chirp can be factored into the form of the solution. Finally, the form of the third-order differential equation that the Jacobi elliptic function satisfies can be applied to a wide range of forms of nonlinearity [2,3,4]. We will elaborate in this talk on the forms of nonlinearity for which this function can be used to produce nontrivial solutions.
References
[1] M. Belic, N. Z. Petrovic, W.-P. Zhong, R. H. Xie and G. Chen, Analytical Light Bullet Solutions to the Generalized (3+1)-Dimensional Nonlinear Schrodinger Equation,Phys. Rev. Lett.101, 0123904 (2008).
[2] N. Z. Petrovic, M. Belic and W.-P. Zhong, Exact traveling-wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional Schrodinger equation with polynomial nonlinearity of arbitrary order, Phys. Rev. E 83, 026604 (2011).
[3] N. Z. Petrovic, Spatiotemporal traveling and solitary wave solutions to the generalized nonlinear Schrodinger equation with single-and dual-power law nonlinearity, Nonlinear Dynamics 93 (4), 2389-2397 (2018)
[4] N. Z. Petrovic, Solitary and traveling wave solutions for the Davey-Stewartson equation using the Jacobi elliptic function expansion method, Optical and Quantum Electronics 52, 1-10 (2020)