Evolution of geometric properties on
solution curve of KdV equation

Ling XU

doi:https://doi.org/10.14445/22315373/IJMTT-V43P505

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 43 | Number 1 | Year 2017 | Article Id. IJMTT-V43P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V43P505

Evolution of geometric properties on solution curve of KdV equation

Ling XU

Citation :

Ling XU, "Evolution of geometric properties on solution curve of KdV equation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 43, no. 1, pp. 20-27, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V43P505

Abstract

This paper discusses some properties of solution curve of the Cauchy problem on the KdV equation by Lagrange coordinate, obtained the evolution consequence of monotonicity, concavity and the isolated extreme points. Namely under the enough smooth condition, the isolated extreme points , monotonicity and convexity of initial solution can be inherited to the solution curve at any t  0. .

Keywords

KdV equation ; solution curve ; monotonicity ; convexity ; isolated extreme point.

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