Solving the modified complex short pulse equation of focusing type: a Riemann-Hilbert approach
type: Item
instance of: scholarly article
title: Solving the modified complex short pulse equation of focusing type: a Riemann-Hilbert approach
author: Yanyan Li
published in: Analysis and Mathematical Physics
publication date: 2022-01-14T00:00:00Z
review text: In this paper, a Riemann-Hilbert approach is presented for the modified complex short pulse equation on the line with zero boundary conditions: \[ u_{xt}=u+\frac{1}{2}u^*(u^2)_{xx},\quad x\in\mathbb{R}, t>0, \] \[ u(x,0)=u_0(x),\quad x\in\mathbb{R} \] where \(u_0(x)\) is a smooth function which decays rapidly as \(x\to\pm\infty\). The Jost solutions of the associated Lax pairs are obtained and the results are used to formulate a matrix Riemann-Hilbert problem suitable for solving the Cauchy problem above. A parametric representation of the solution to the related Cauchy problem is obtained. Consequently, soliton solutions are constructed using the formalism of the Riemann-Hilbert problem.
reviewed by: Solomon Manukure
Mathematics Subject Classification ID: 35Q51
Mathematics Subject Classification ID: 35Q15
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 37K15
Mathematics Subject Classification ID: 37K35
Mathematics Subject Classification ID: 35C08
zbMATH DE Number: 7457156
zbMATH Keywords: modified complex short pulse equation
zbMATH Keywords: Riemann-Hilbert problem
zbMATH Keywords: Lax pairs
zbMATH Keywords: soliton solutions
MaRDI profile type: Publication
full work available at URL: s13324-021-00637-7
OpenAlex ID: W4206254496
Wikidata QID: Q114220024
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DOI: 10.1007/S13324-021-00637-7
description: scientific article; zbMATH DE number 7457156