A Riemann-Hilbert approach to solution of the modified focusing complex short pulse equation

被引：1
|
作者：
Barkov, Ruslan [1 ]
Shepelsky, Dmitry [1 ,2 ]
机构：
[1] Kharkov Natl Univ, Sch Math & Comp Sci, Kharkiv, Ukraine
[2] B Verkin Inst Low Temp Phys & Engn, Math Div, Kharkiv, Ukraine
来源：
FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS | 2024年 / 10卷
关键词：
short pulse equation; short wave equation; Camassa-Holm-type equation; inverse scattering transform; Riemann-Hilbert problem;
D O I：
10.3389/fams.2024.1466965
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We develop a Riemann-Hilbert approach to the modified focusing complex short pulse (mfcSP) equationuxt=u+12u<overline>(u2)xxwith zero boundary conditions (as |x| -> infinity). We obtain a parametric representation of the solution of the initial value problem for the mfcSP equation in terms of the solution of the associated Riemann-Hilbert problem. This representation is then used for retrieving one-soliton solutions.
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页数：14
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