Nonexistence and uniqueness of breathers for modified Zakharov-Kuznetsov models.

Abstract:

In this talk we will consider the (focusing) modied Zakharov-Kuznetsov (mZK) in dimension N ≥ 1: ut + (∆u + 2u3)x1 = 0,for a given real-valued function u = u(t, x), where t ∈ R and x ∈ RN . This equation is a specialcase of the completely integrable modied Korteweg-de Vries (mKdV) equation ut + (uxx +2u3)x = 0. During this talk we will present results related to existence and nonexistence of

quasimonochromatic breathers solution for the mZK equation, depending on the dimnesion N .

Additionally we will show how the famous breather solution of the mKdV equation representsa unique instance of a quasimonochromatic breathers solution

Posted on Jan 17, 2025 in Differential Equations, Seminars