Publication Information

{'id': 'https://openalex.org/W1973657206', 'doi': 'https://doi.org/10.1088/0253-6102/56/4/23', 'title': 'Mathieu Progressive Waves', 'display_name': 'Mathieu Progressive Waves', 'publication_year': 2011, 'publication_date': '2011-10-01', 'ids': {'openalex': 'https://openalex.org/W1973657206', 'doi': 'https://doi.org/10.1088/0253-6102/56/4/23', 'mag': '1973657206'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1088/0253-6102/56/4/23', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S165969127', 'display_name': 'Communications in Theoretical Physics', 'issn_l': '0253-6102', 'issn': ['0253-6102', '1572-9494'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310311669', 'host_organization_name': 'Institute of Physics', 'host_organization_lineage': ['https://openalex.org/P4310311669'], 'host_organization_lineage_names': ['Institute of Physics'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5085620793', 'display_name': 'Andrei B. Utkin', 'orcid': 'https://orcid.org/0000-0002-4656-3314'}, 'institutions': [{'id': 'https://openalex.org/I141596103', 'display_name': 'University of Lisbon', 'ror': 'https://ror.org/01c27hj86', 'country_code': 'PT', 'type': 'education', 'lineage': ['https://openalex.org/I141596103']}], 'countries': ['PT'], 'is_corresponding': True, 'raw_author_name': 'Andrei B. Utkin', 'raw_affiliation_strings': ['ICEMS, Institute Superior Técnico, Tecnical University of Lisbon, Av. Rovisco Pais 1, Lisbon 1049-001, Portugal'], 'affiliations': [{'raw_affiliation_string': 'ICEMS, Institute Superior Técnico, Tecnical University of Lisbon, Av. Rovisco Pais 1, Lisbon 1049-001, Portugal', 'institution_ids': ['https://openalex.org/I141596103']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5085620793'], 'corresponding_institution_ids': ['https://openalex.org/I141596103'], 'apc_list': None, 'apc_paid': None, 'fwci': 0.489, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 3, 'citation_normalized_percentile': {'value': 0.488702, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 76, 'max': 78}, 'biblio': {'volume': '56', 'issue': '4', 'first_page': '733', 'last_page': '739'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10490', 'display_name': 'Orbital Angular Momentum in Optics', 'score': 0.993, 'subfield': {'id': 'https://openalex.org/subfields/3107', 'display_name': 'Atomic and Molecular Physics, and Optics'}, '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/T10490', 'display_name': 'Orbital Angular Momentum in Optics', 'score': 0.993, 'subfield': {'id': 'https://openalex.org/subfields/3107', 'display_name': 'Atomic and Molecular Physics, and Optics'}, '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/T10988', 'display_name': 'Advanced Fiber Laser Technologies', 'score': 0.9902, 'subfield': {'id': 'https://openalex.org/subfields/3107', 'display_name': 'Atomic and Molecular Physics, and Optics'}, '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/T11261', 'display_name': 'Quantum chaos and dynamical systems', 'score': 0.9864, '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/elliptic-coordinate-system', 'display_name': 'Elliptic coordinate system', 'score': 0.9067508}, {'id': 'https://openalex.org/keywords/bipolar-coordinates', 'display_name': 'Bipolar coordinates', 'score': 0.61438924}, {'id': 'https://openalex.org/keywords/mathieu-function', 'display_name': 'Mathieu function', 'score': 0.6054879}, {'id': 'https://openalex.org/keywords/parabolic-coordinates', 'display_name': 'Parabolic coordinates', 'score': 0.56448466}, {'id': 'https://openalex.org/keywords/separation-of-variables', 'display_name': 'Separation of variables', 'score': 0.51180714}, {'id': 'https://openalex.org/keywords/limiting', 'display_name': 'Limiting', 'score': 0.4113665}], 'concepts': [{'id': 'https://openalex.org/C98343798', 'wikidata': 'https://www.wikidata.org/wiki/Q1790208', 'display_name': 'Curvilinear coordinates', 'level': 2, 'score': 0.92287004}, {'id': 'https://openalex.org/C108172862', 'wikidata': 'https://www.wikidata.org/wiki/Q1332432', 'display_name': 'Elliptic coordinate system', 'level': 3, 'score': 0.9067508}, {'id': 'https://openalex.org/C27451561', 'wikidata': 'https://www.wikidata.org/wiki/Q2588831', 'display_name': 'Orthogonal coordinates', 'level': 2, 'score': 0.74775267}, {'id': 'https://openalex.org/C107706756', 'wikidata': 'https://www.wikidata.org/wiki/Q219637', 'display_name': 'Bessel function', 'level': 2, 'score': 0.73142403}, {'id': 'https://openalex.org/C201076478', 'wikidata': 'https://www.wikidata.org/wiki/Q211851', 'display_name': 'Cylindrical coordinate system', 'level': 2, 'score': 0.6155723}, {'id': 'https://openalex.org/C206647686', 'wikidata': 'https://www.wikidata.org/wiki/Q2383591', 'display_name': 'Bipolar coordinates', 'level': 3, 'score': 0.61438924}, {'id': 'https://openalex.org/C157097347', 'wikidata': 'https://www.wikidata.org/wiki/Q1908689', 'display_name': 'Mathieu function', 'level': 2, 'score': 0.6054879}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.592253}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.59042364}, {'id': 'https://openalex.org/C126990412', 'wikidata': 'https://www.wikidata.org/wiki/Q203218', 'display_name': 'Spherical coordinate system', 'level': 2, 'score': 0.5794604}, {'id': 'https://openalex.org/C80551277', 'wikidata': 'https://www.wikidata.org/wiki/Q11210', 'display_name': 'Coordinate system', 'level': 2, 'score': 0.576965}, {'id': 'https://openalex.org/C113504408', 'wikidata': 'https://www.wikidata.org/wiki/Q2373660', 'display_name': 'Parabolic coordinates', 'level': 4, 'score': 0.56448466}, {'id': 'https://openalex.org/C159722891', 'wikidata': 'https://www.wikidata.org/wiki/Q913323', 'display_name': 'Separation of variables', 'level': 3, 'score': 0.51180714}, {'id': 'https://openalex.org/C188198153', 'wikidata': 'https://www.wikidata.org/wiki/Q1613840', 'display_name': 'Limiting', 'level': 2, 'score': 0.4113665}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.32248348}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.30636752}, {'id': 'https://openalex.org/C136364276', 'wikidata': 'https://www.wikidata.org/wiki/Q6666761', 'display_name': 'Log-polar coordinates', 'level': 3, 'score': 0.23416132}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.09288204}, {'id': 'https://openalex.org/C93779851', 'wikidata': 'https://www.wikidata.org/wiki/Q271977', 'display_name': 'Partial differential equation', 'level': 2, 'score': 0.09045681}, {'id': 'https://openalex.org/C78519656', 'wikidata': 'https://www.wikidata.org/wiki/Q101333', 'display_name': 'Mechanical engineering', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C127413603', 'wikidata': 'https://www.wikidata.org/wiki/Q11023', 'display_name': 'Engineering', 'level': 0, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1088/0253-6102/56/4/23', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S165969127', 'display_name': 'Communications in Theoretical Physics', 'issn_l': '0253-6102', 'issn': ['0253-6102', '1572-9494'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310311669', 'host_organization_name': 'Institute of Physics', 'host_organization_lineage': ['https://openalex.org/P4310311669'], 'host_organization_lineage_names': ['Institute of Physics'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [{'score': 0.63, 'display_name': 'Sustainable cities and communities', 'id': 'https://metadata.un.org/sdg/11'}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 23, 'referenced_works': ['https://openalex.org/W1578004187', 'https://openalex.org/W1680579736', 'https://openalex.org/W1964591703', 'https://openalex.org/W1975791259', 'https://openalex.org/W1995144131', 'https://openalex.org/W1996160600', 'https://openalex.org/W1999597579', 'https://openalex.org/W2001348549', 'https://openalex.org/W2002236303', 'https://openalex.org/W2008476021', 'https://openalex.org/W2025063762', 'https://openalex.org/W2032028897', 'https://openalex.org/W2032231305', 'https://openalex.org/W2033724763', 'https://openalex.org/W2034701496', 'https://openalex.org/W2054594825', 'https://openalex.org/W2068941137', 'https://openalex.org/W2082159216', 'https://openalex.org/W2104900371', 'https://openalex.org/W2624183933', 'https://openalex.org/W4212986059', 'https://openalex.org/W4231480853', 'https://openalex.org/W4300223101'], 'related_works': ['https://openalex.org/W993586985', 'https://openalex.org/W3023944961', 'https://openalex.org/W2734289321', 'https://openalex.org/W2508439853', 'https://openalex.org/W2375052559', 'https://openalex.org/W2148002435', 'https://openalex.org/W2072720735', 'https://openalex.org/W2017047985', 'https://openalex.org/W1679597514', 'https://openalex.org/W1144615322'], 'abstract_inverted_index': {'A': [0], 'new': [1], 'family': [2], 'of': [3, 19, 28, 35, 52, 55, 72, 96], 'exact': [4], 'solutions': [5], 'to': [6, 89, 91], 'the': [7, 22, 29, 56, 64, 77, 92, 97], 'wave': [8, 94], 'equation': [9], 'representing': [10], 'relatively': [11], 'undistorted': [12], 'progressive': [13], 'waves': [14], 'is': [15, 46, 67, 87], 'constructed': [16], 'using': [17], 'separation': [18], 'variables': [20], 'in': [21, 39, 75], 'elliptic': [23, 78], 'cylindrical': [24, 43, 79, 85], 'coordinates': [25, 80], 'and': [26, 48], 'one': [27], 'Bateman': [30, 37], 'transforms.': [31], 'The': [32, 69], 'general': [33], 'form': [34], 'this': [36], 'transform': [38], 'an': [40], 'orthogonal': [41], 'curvilinear': [42], 'coordinate': [44], 'system': [45], 'discussed': [47], 'a': [49], 'specific': [50], 'problem': [51], 'physical': [53], 'feasibility': [54], 'obtained': [57], 'solutions,': [58], 'connected': [59], 'with': [60], 'their': [61, 83], 'dependence': [62], 'on': [63], 'cyclic': [65], 'coordinate,': [66], 'addressed.': [68], 'limiting': [70], 'case': [71], 'zero': [73], 'eccentricity,': [74], 'which': [76], 'turn': [81], 'into': [82], 'circular': [84], 'counterparts,': [86], 'shown': [88], 'correspond': [90], 'focused': [93], 'modes': [95], 'Bessel-Gauss': [98], 'type.': [99]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W1973657206', 'counts_by_year': [{'year': 2014, 'cited_by_count': 1}, {'year': 2013, 'cited_by_count': 1}, {'year': 2012, 'cited_by_count': 1}], 'updated_date': '2024-12-07T18:06:31.871507', 'created_date': '2016-06-24'}