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

Ruslan Barkov; Dmitry Shepelsky; Dmitry Shepelsky

doi:10.3389/fams.2024.1466965

Frontiers in Applied Mathematics and Statistics (Aug 2024)

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

Ruslan Barkov,
Dmitry Shepelsky,
Dmitry Shepelsky

Affiliations

Ruslan Barkov: School of Mathematics and Computer Sciences, V. N. Karazin Kharkiv National University, Kharkiv, Ukraine
Dmitry Shepelsky: School of Mathematics and Computer Sciences, V. N. Karazin Kharkiv National University, Kharkiv, Ukraine
Dmitry Shepelsky: Mathematical Division, B. Verkin Institute for Low Temperature Physics and Engineering, Kharkiv, Ukraine

DOI: https://doi.org/10.3389/fams.2024.1466965
Journal volume & issue: Vol. 10

Abstract

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We develop a Riemann–Hilbert approach to the modified focusing complex short pulse (mfcSP) equationuxt=u+12u¯(u2)xxwith zero boundary conditions (as |x| → ∞). 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.

Published in Frontiers in Applied Mathematics and Statistics

ISSN: 2297-4687 (Online)
Publisher: Frontiers Media S.A.
Country of publisher: Switzerland
LCC subjects: Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods; Science: Mathematics: Probabilities. Mathematical statistics
Website: http://journal.frontiersin.org/journal/applied-mathematics-and-statistics#

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