The long-time asymptotics of the derivative nonlinear Schr<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e934" altimg="si9.svg"><mml:mover accent="true"><mml:mrow><mml:mi mathvariant="normal">o</mml:mi></mml:mrow><mml:mrow><mml:mo>̈</mml:mo></mml:mrow></mml:mover></mml:math>dinger equation with step-like initial value
نویسندگان
چکیده
Consideration in this present paper is the long-time asymptotics of solutions to derivative nonlinear Schrödinger (DNLS) equation with step-like initial value q(x,0)=q0(x)=A1eiϕe2iBx,x<0,A2e−2iBx,x>0,by Deift-Zhou method. The problem described by a matrix Riemann-Hilbert problem. A crucial ingredient used introduce g-function mechanism for solving entries jump growing exponentially as t→∞. It shown that leading order term solution DNLS expressed Theta function Θ about Riemann-surface genus 3 and subleading parabolic cylinder Airy functions.
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15 صفحه اولextensions of some polynomial inequalities to the polar derivative
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ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 2023
ISSN: ['1872-8022', '0167-2789']
DOI: https://doi.org/10.1016/j.physd.2023.133855