L. K. Arruda and D.E. Pelinovsky
Kink breathers on a traveling wave background in the defocusing MKDV equation
Abstract:
We characterize a general traveling periodic wave of the defocusing mKdV (modified Korteweg-de Vries)
equation by using a quotient of products of Jacobi's elliptic theta functions.
Compared to the standing periodic wave of the defocusing NLS (nonlinear Schrodinger)
equation, these solutions are special cases of Riemann's theta function of genus two. Based
on our characterization, we derive a new two-parameter solution form which defines a general
three-parameter solution form with the scaling transformation. Eigenfunctions of the Lax
system for the general traveling periodic wave are also characterized as quotients of products
of Jacobi's theta functions. As the main outcome of our analytical computations, we derive a
new solution of the defocusing mKdV equation which describes the kink breather propagating
on a general traveling wave background.
Keywords:
modified Korteweg-de Vries equation, elliptic traveling waves, kink breathers,
Darboux transformation, Jacobi's theta functions.