6 papers
Painlevé XXXIV Asymptotics for the Focusing mKdV Equation with Finite-Genus Background and Discrete Spectrum
Ruihong Ma, Engui Fan
We investigate the Cauchy problem for the focusing modified Korteweg--de Vries (mKdV) equation with finite-genus algebro-geometric quasi-periodic initial data. By applying the nonl…
Painlevé Asymptotics of the Focusing Nonlinear Schrödinger Equation with a Finite-Genus Algebro-Geometric Background
Ruihong ma, Engui Fan
We investigate the Cauchy problem for the focusing nonlinear Schrödinger (NLS) equation \begin{equation} iq_t(x,t)+q_{xx}(x,t)+2|q(x,t)|^2q(x,t)=0,\quad x\in\mathbb{R},\quad t\ge0,…
Soliton Shielding of the focusing modified KdV equation
Ruihong Ma, Engui Fan
We consider soliton gas solutions of the modified Korteweg-de Vries (mKdV) equation, where the point spectrum of the condensate is located within a bounded domain in the upper half…
Soliton resolution and asymptotic stability of -loop-soliton solutions for the Ostrovsky-Vakhnenko equation
Ruihong Ma, Engui Fan
The Ostrovsky-Vakhnenko (OV) equation \begin{align*} &u_{txx}-3κu_x+3u_xu_{xx}+uu_{xxx}=0 \end{align*} is a short wave model of the well-known Degasperis-Procesi equation and admit…
The asymptotic stability of solitons in the focusing Hirota equation on the line
Ruihong Ma, Engui Fan
In this paper, the -steepest descent method and Bäcklund transformation are used to study the asymptotic stability of solitons to the Cauchy problem of focusing…
Long time asymptotics behavior of the focusing nonlinear Kundu-Eckhaus equation
Ruihong Ma, Engui Fan
We study the Cauchy problem for the focusing nonlinear Kundu-Eckhaus equation and construct long time asymptotic expansion of its solution in fixed space-time cone with $C(x_1,x_2,…