{"id":"https://openalex.org/G6989481663","display_name":"Analysis of concentration  phenomena for nonlinear wave and dispersive equations","description":"The well-posedness of the initial value problem is the most fundamental problem in the field of nonlinear evolution equations. The well-posedness is a concept consisting of three properties: existence of solution, uniqueness and continuous dependence of solutions on initial data. It heavily depends on the sturacture of each nonlinear evolution equation when its initial value problem is well-posed, which is very attractive.  The study of the structure for each important equation has a great significance, since it is extremely difficult to construct the general theory applicable to various nonlinear evolution equations. In this research, we study the well-posedness of the initial value problem for the nonlinear Schroedinger equation with Ramman scattering term and the kinetic derivative nonlinear Schroedinger equation. We have showed that the well-posedness depends on the regularity of function spaces to which solutions belong.","funder_award_id":"17H02853","funder":{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","doi":"10.13039/501100001691"},"funded_outputs":["https://openalex.org/W2571610035","https://openalex.org/W2804694594","https://openalex.org/W2886912241","https://openalex.org/W2911194176","https://openalex.org/W2950897072","https://openalex.org/W2962743920","https://openalex.org/W2962915878","https://openalex.org/W2963351503","https://openalex.org/W2963927963","https://openalex.org/W2964334256","https://openalex.org/W2970440122","https://openalex.org/W2970869126","https://openalex.org/W2975981742","https://openalex.org/W2986458125","https://openalex.org/W2994766364","https://openalex.org/W3003638555","https://openalex.org/W3044864483","https://openalex.org/W3097353916","https://openalex.org/W3099316863","https://openalex.org/W3143440440","https://openalex.org/W3186503736","https://openalex.org/W3191050321","https://openalex.org/W3194238786","https://openalex.org/W3197804530","https://openalex.org/W3200969857","https://openalex.org/W3210883283","https://openalex.org/W3216786208","https://openalex.org/W4200184478","https://openalex.org/W4213205870","https://openalex.org/W4224093773","https://openalex.org/W4306842241","https://openalex.org/W4319316404","https://openalex.org/W4377247637","https://openalex.org/W4384941031","https://openalex.org/W4414436223","https://openalex.org/W7143873284"],"funded_outputs_count":36,"parent_awards":[],"sub_awards":[],"sub_awards_count":0,"amount":17680000.0,"currency":"JPY","amount_usd":158106.97,"amount_usd_basis":"daily_rate","recipients":[],"recipient_countries":[],"recipient_regions":[],"research_scope":{"is_research":true,"basis":"funder_default","tier":1},"funding_type":"research","funder_scheme":"Grant-in-Aid for Scientific Research (B)","start_date":"2017-04-01","end_date":"2022-03-31","start_year":2017,"end_year":2022,"landing_page_url":"https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17H02853/","doi":null,"provenance":"kaken","lead_investigator":{"given_name":"Yoshio","family_name":"Tsutsumi","orcid":null,"role_start":null,"affiliation":{"name":"Kyoto University","country":"Japan","ids":[{"id":"https://nrid.nii.ac.jp/nrid/1000010180027","type":"nrid","asserted_by":"kaken"}]}},"co_lead_investigator":null,"investigators":null,"works_api_url":"https://api.openalex.org/works?filter=awards.id:G6989481663","primary_topic":null,"topics":null,"institution_awarded":[{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]}],"updated_date":"2026-10-16T03:01:01.000Z","created_date":"2026-07-13T04:17:19.000Z"}