2011/05/31 by Cheng-shi Liu, Liu, Cheng-shi
Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Numerical methods for differential equations #math.CA #nlin.SI
paper · pdf · doi:10.48550/arxiv.1105.6175
arxiv created 2011/05/31 · openalex publication_date 2011/05/31 · arxiv updated 2011/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Elliptic equation (y')2=a0+a2y2+a4y4 is the foundation of the elliptic function expansion method of finding exact solutions to nonlinear differential equation. In some references, some new form solutions to the elliptic equation have been claimed. In the paper, we discuss its solutions in detail. By detailed computation, we prove that those new form solutions can be derived from a very few known solutions. This means that those new form solutions are just new representations of old solutions. From our discussion, some new identities of the elliptic function can be obtained. In the course of discussion, we give an example of this kind of formula.