{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T03:40:41Z","timestamp":1777002041246,"version":"3.51.4"},"reference-count":21,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T00:00:00Z","timestamp":1724976000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Appl. Math. Stat."],"abstract":"<jats:p>We develop a Riemann\u2013Hilbert approach to the modified focusing complex short pulse (mfcSP) equation<\/jats:p><jats:p><jats:disp-formula><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msub><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>x<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo>=<\/mml:mo><mml:mi>u<\/mml:mi><mml:mo>+<\/mml:mo><mml:mfrac><mml:mrow><mml:mn>1<\/mml:mn><\/mml:mrow><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:mfrac><mml:mover accent=\"true\"><mml:mi>u<\/mml:mi><mml:mo>\u00af<\/mml:mo><\/mml:mover><mml:msub><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:mrow><mml:mrow><mml:mi>x<\/mml:mi><mml:mi>x<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math><\/jats:disp-formula><\/jats:p><jats:p>with zero boundary conditions (as |<jats:italic>x<\/jats:italic>| \u2192 \u221e). 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\u2013Hilbert problem. This representation is then used for retrieving one-soliton solutions.<\/jats:p>","DOI":"10.3389\/fams.2024.1466965","type":"journal-article","created":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T04:49:38Z","timestamp":1724993378000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["A Riemann\u2013Hilbert approach to solution of the modified focusing complex short pulse equation"],"prefix":"10.3389","volume":"10","author":[{"given":"Ruslan","family":"Barkov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dmitry","family":"Shepelsky","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1965","published-online":{"date-parts":[[2024,8,30]]},"reference":[{"key":"B1","volume-title":"Solitons and the Inverse Scattering Transform. 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