{"corpus_id":126450919,"paper_sha":"bfc7b6968219b7b3a8cdeed86400fbcf139617a8","doi":"10.1002/mma.5512","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":2913026731,"dblp_id":null,"acl_id":null,"title":"Complexiton solutions to the Hirota‐Satsuma‐Ito equation","year":2019,"publication_date":"2019-02-03","venue":"Mathematical methods in the applied sciences","journal":{"name":"Mathematical Methods in the Applied Sciences","pages":"2344 - 2351","volume":"42"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics","Physics"],"reference_count":25,"citation_count":42,"influential_citation_count":0,"is_open_access":false,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"The Hirota bilinear method is a powerful tool for solving nonlinear evolution equations. Together with the linear superposition principle, it can be used to find a special class of explicit solutions that correspond to complex eigenvalues of associated characteristic problems. These solutions are known as complexiton solutions or simply complexitons. In this article, we study complexiton solutions of the the Hirota‐Satsuma‐Ito equation which is a (2 + 1)‐dimensional extension of the Hirota‐Satsuma shallow water wave equation known to describe propagation of unidirectional shallow water waves. We first construct hyperbolic function solutions and consequently derive the so‐called complexitons via the Hirota bilinear method and the linear superposition principle. In particular, we find nonsingular complexiton solutions to the Hirota‐Satsuma‐Ito equation. Finally, we give some illustrative examples and a few concluding remarks.","claims":[{"public_id":"cl_3a33b57d143ab2d94c5a873db0735648","status":"active","text":"Complexiton solutions are derived for the Hirota-Satsuma-Ito equation from the constructed hyperbolic function solutions.","confidence":0.95,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_3a33b57d143ab2d94c5a873db0735648"},{"public_id":"cl_b265a2242bf719efc8d3006f808d085b","status":"active","text":"Hyperbolic function solutions can be constructed for the Hirota-Satsuma-Ito equation using the Hirota bilinear method and the linear superposition principle.","confidence":0.97,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous 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