{"id":"https://openalex.org/W7204807319","doi":"https://doi.org/10.48550/arxiv.2608.28077","title":"A Local Discontinuous Galerkin method for the modified Camassa--Holm equation","display_name":"A Local Discontinuous Galerkin method for the modified Camassa--Holm equation","publication_year":2026,"publication_date":"2026-08-28","ids":{"openalex":"https://openalex.org/W7204807319","doi":"https://doi.org/10.48550/arxiv.2608.28077"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.28077","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28077","pdf_url":"https://arxiv.org/pdf/2608.28077","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,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.28077","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025248530","display_name":"Xiang\u2010Ke Chang","orcid":"https://orcid.org/0000-0003-0056-8619","observed_orcids":["https://orcid.org/0000-0003-0056-8619"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chang, Xiang-Ke","raw_affiliation_strings":["ICMSEC , State Key Laboratory of Mathematical Sciences (SKLMS) , Academy of Mathematics and Systems Science , and School of Mathematical Science , University of Chinese Academy of Sciences , Chinese Academy of Sciences , Beijing 100190 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ICMSEC , State Key Laboratory of Mathematical Sciences (SKLMS) , Academy of Mathematics and Systems Science , and School of Mathematical Science , University of Chinese Academy of Sciences , Chinese Academy of Sciences , Beijing 100190 , P. R. China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485","https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148817527","display_name":"Yong Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Yong","raw_affiliation_strings":["ICMSEC , State Key Laboratory of Mathematical Sciences (SKLMS) , Academy of Mathematics and Systems Science , and School of Mathematical Science , University of Chinese Academy of Sciences , Chinese Academy of Sciences , Beijing 100190 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ICMSEC , State Key Laboratory of Mathematical Sciences (SKLMS) , Academy of Mathematics and Systems Science , and School of Mathematical Science , University of Chinese Academy of Sciences , Chinese Academy of Sciences , Beijing 100190 , P. R. China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485","https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100637106","display_name":"Qi Tao","orcid":"https://orcid.org/0000-0003-3041-7299","observed_orcids":["https://orcid.org/0000-0003-3041-7299"]},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao, Qi","raw_affiliation_strings":["School of Mathematics, Statistics and Mechanics , Beijing University of Technol- ogy , Beijing 100124 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Statistics and Mechanics , Beijing University of Technol- ogy , Beijing 100124 , P. R. China","institution_ids":["https://openalex.org/I37796252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.5429999828338623,"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"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.5429999828338623,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.28859999775886536,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.093299999833107,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/local-discontinuous-galerkin-method","display_name":"local discontinuous Galerkin method","score":0.9739999771118164},{"id":"https://openalex.org/keywords/modified-camassa-holm-equation","display_name":"modified Camassa-Holm equation","score":0.9990000128746033},{"id":"https://openalex.org/keywords/kerr-nonlinearity","display_name":"Kerr nonlinearity","score":0.8650000095367432},{"id":"https://openalex.org/keywords/energy-conservation-physics","display_name":"energy conservation (physics)","score":0.9459999799728394},{"id":"https://openalex.org/keywords/dissipative-fluxes","display_name":"dissipative fluxes","score":0.8299999833106995},{"id":"https://openalex.org/keywords/error-estimates","display_name":"error estimates","score":0.8510000109672546},{"id":"https://openalex.org/keywords/peakon-solutions","display_name":"peakon solutions","score":0.8820000290870667},{"id":"https://openalex.org/keywords/nonlinear-wave-equations","display_name":"nonlinear wave equations","score":0.46700000762939453}],"concepts":[{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7851999998092651},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.6966000199317932},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6696000099182129},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.614300012588501},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.569100022315979},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5468999743461609},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5288000106811523},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4528999924659729},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.42649999260902405},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.38040000200271606},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.36250001192092896},{"id":"https://openalex.org/C2989268449","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Energy method","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.3240000009536743},{"id":"https://openalex.org/C52957995","wikidata":"https://www.wikidata.org/wiki/Q11382","display_name":"Conservation of energy","level":2,"score":0.3149000108242035},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.31470000743865967},{"id":"https://openalex.org/C175221391","wikidata":"https://www.wikidata.org/wiki/Q5281666","display_name":"Discontinuous Deformation Analysis","level":3,"score":0.2992999851703644},{"id":"https://openalex.org/C520301825","wikidata":"https://www.wikidata.org/wiki/Q380170","display_name":"Energy conservation","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2948000133037567},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.2842000126838684},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.2736999988555908},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C3020065929","wikidata":"https://www.wikidata.org/wiki/Q11379","display_name":"Total energy","level":3,"score":0.25690001249313354},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.2549999952316284}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.28077","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28077","pdf_url":"https://arxiv.org/pdf/2608.28077","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,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.28077","doi":"https://doi.org/10.48550/arxiv.2608.28077","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.28077","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,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.28077","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28077","pdf_url":"https://arxiv.org/pdf/2608.28077","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,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2856102575","display_name":null,"funder_award_id":"12288201","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G3027066466","display_name":null,"funder_award_id":"12301464","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7236627023","display_name":null,"funder_award_id":"12571395","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G790494869","display_name":null,"funder_award_id":"XDB0640000","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G8533620077","display_name":null,"funder_award_id":"12288201","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"},{"id":"https://openalex.org/F4320335892","display_name":"Youth Innovation Promotion Association","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204807319.pdf","grobid_xml":"https://content.openalex.org/works/W7204807319.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1986208932","https://openalex.org/W7099999432","https://openalex.org/W2884756172","https://openalex.org/W4293473500","https://openalex.org/W4410879183","https://openalex.org/W2905189568","https://openalex.org/W4404528136","https://openalex.org/W4361301421","https://openalex.org/W2054768480","https://openalex.org/W2468131123"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"propose":[4],"a":[5],"local":[6],"discontinuous":[7],"Galerkin":[8],"(LDG)":[9],"method":[10,61],"for":[11],"the":[12,32,42,58,66,70],"modified":[13],"Camassa-Holm":[14],"(mCH)":[15],"equation":[16],"that":[17,51],"contains":[18],"cubic":[19],"nonlinearity":[20],"and":[21,27,34,57],"high-order":[22],"derivative":[23],"terms.":[24],"Energy":[25],"conservation":[26],"stability":[28],"are":[29,55],"obtained":[30],"using":[31],"conservative":[33],"dissipative":[35],"fluxes,":[36],"respectively.":[37],"The":[38],"error":[39],"estimate":[40],"of":[41,64,69],"semi-discrete":[43],"scheme":[44],"is":[45,62],"also":[46],"established.":[47],"Numerical":[48],"examples":[49],"verify":[50],"our":[52],"theoretical":[53],"findings":[54],"sharp":[56],"proposed":[59],"LDG":[60],"capable":[63],"capturing":[65],"peakon":[67],"solution":[68],"mCH":[71],"equation.":[72]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-01T00:00:00"}
