{"id":"https://openalex.org/W7162334813","doi":"https://doi.org/10.48550/arxiv.2605.23181","title":"High-order Conservative Discontinuous Galerkin Methods via Implicit Penalization for the Generalized Korteweg-de Vries Equation and the Hirota-Satsuma KdV System","display_name":"High-order Conservative Discontinuous Galerkin Methods via Implicit Penalization for the Generalized Korteweg-de Vries Equation and the Hirota-Satsuma KdV System","publication_year":2026,"publication_date":"2026-05-22","ids":{"openalex":"https://openalex.org/W7162334813","doi":"https://doi.org/10.48550/arxiv.2605.23181"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.23181","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.23181","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.23181","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136979123","display_name":"M. Shan Tariq","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tariq, M. Shan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041162676","display_name":"Yanlai Chen","orcid":"https://orcid.org/0000-0002-7460-8313"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Yanlai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101734720","display_name":"Bo Dong","orcid":"https://orcid.org/0000-0003-4067-3763"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dong, Bo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.42559999227523804,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.42559999227523804,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.2506999969482422,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.14079999923706055,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.8184999823570251},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6226000189781189},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5769000053405762},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5702999830245972},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.4950999915599823},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.4731000065803528},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4625000059604645},{"id":"https://openalex.org/keywords/conservation-of-mass","display_name":"Conservation of mass","score":0.4307999908924103},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.40230000019073486}],"concepts":[{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.8184999823570251},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.691100001335144},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6226000189781189},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5769000053405762},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5702999830245972},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5346999764442444},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.4950999915599823},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.4731000065803528},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4625000059604645},{"id":"https://openalex.org/C157206272","wikidata":"https://www.wikidata.org/wiki/Q483948","display_name":"Conservation of mass","level":2,"score":0.4307999908924103},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.40230000019073486},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3741999864578247},{"id":"https://openalex.org/C52957995","wikidata":"https://www.wikidata.org/wiki/Q11382","display_name":"Conservation of energy","level":2,"score":0.36980000138282776},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.351500004529953},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.3472000062465668},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.3441999852657318},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3337000012397766},{"id":"https://openalex.org/C520301825","wikidata":"https://www.wikidata.org/wiki/Q380170","display_name":"Energy conservation","level":2,"score":0.32600000500679016},{"id":"https://openalex.org/C3019693144","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Time stepping","level":3,"score":0.3188000023365021},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.3057999908924103},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.2856999933719635},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.2800999879837036},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25529998540878296},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.2551000118255615},{"id":"https://openalex.org/C2989268449","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Energy method","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.23181","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.23181","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.23181","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.23181","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"display_name":"Life in Land","score":0.5075517296791077,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"develop":[1],"new":[2,96],"conservative":[3,67,145],"discontinuous":[4],"Galerkin":[5],"(DG)":[6],"methods":[7,29],"for":[8,70,119,179],"nonlinear":[9,127],"wave":[10],"problems,":[11],"focusing":[12],"on":[13],"the":[14,21,33,52,71,78,82,85,109,117,133,137,143,154,160,167,181],"generalized":[15],"Korteweg-de":[16],"Vries":[17],"(gKdV)":[18],"equation":[19,183],"and":[20,41,123,162,175,184],"coupled":[22,138],"Hirota-Satsuma":[23],"KdV":[24],"(HS-KdV)":[25],"system.":[26,186],"The":[27],"proposed":[28,168],"preserve":[30],"mass":[31],"through":[32,55],"single-valued":[34],"structure":[35],"of":[36,81,84,153,166],"numerical":[37,53],"traces,":[38],"while":[39],"energy":[40],"Hamiltonian":[42],"conservation":[43,57,177],"are":[44],"enforced":[45],"by":[46,101],"implicitly":[47],"determining":[48],"penalty":[49],"parameters":[50],"in":[51],"traces":[54],"auxiliary":[56],"constraints.":[58],"In":[59],"our":[60],"previous":[61,134],"work":[62],"[11],":[63],"we":[64,141],"developed":[65],"a":[66,103],"DG":[68,146],"method":[69,147],"gKdV":[72,182],"equation;":[73],"however,":[74],"that":[75,107,148],"formulation":[76,97],"involves":[77],"time":[79,121,130],"derivative":[80],"jump":[83],"approximate":[86],"solution,":[87],"which":[88],"complicates":[89],"extensions":[90],"beyond":[91],"second-order":[92],"temporal":[93],"accuracy.":[94],"Our":[95],"overcomes":[98],"this":[99],"limitation":[100],"introducing":[102],"redesigned":[104],"trace":[105],"configuration":[106],"eliminates":[108],"derivative-of-jump":[110],"term.":[111],"This":[112],"novel":[113],"enhancement":[114],"seamlessly":[115],"paves":[116],"way":[118],"higher-order":[120],"discretizations":[122],"requires":[124],"solving":[125],"fewer":[126],"systems":[128],"per":[129],"step":[131],"than":[132],"approach.":[135],"For":[136],"HS-KdV":[139,185],"system,":[140],"present":[142],"first":[144],"preserves":[149],"all":[150],"three":[151],"invariants":[152],"exact":[155],"solution.":[156],"Numerical":[157],"results":[158],"demonstrate":[159],"accuracy":[161],"expected":[163],"convergence":[164],"behavior":[165],"methods,":[169],"as":[170,172],"well":[171],"long-time":[173],"stability":[174],"strong":[176],"properties":[178],"both":[180]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-26T00:00:00"}