c06033402ec2b95b3b79f6e8a1d4a7d5 mathematics-11-04545-v2.pdf 33e1e958257484de53b37cd4e3048c82d161c5eb mathematics-11-04545-v2.pdf 0102b0b86a777f9ee74ffa633e93a075246de3b0edfee4e171160ccbcc69067e mathematics-11-04545-v2.pdf Title: Integrability Properties of the Slepyan–Palmov Model Arising in the Slepyan–Palmov Medium Subject: This study investigates the Slepyan–Palmov (SP) model, which describes plane longitudinal waves propagating within a medium comprising a carrier medium and nonlinear oscillators. The primary objective is to analyze the integrability properties of this model. The research entails two key aspects. Firstly, the study explores the group invariant solution by utilizing reductions in symmetry subalgebras based on the optimal system. Secondly, the conservation laws are studied using the homotopy operator, which offers advantages over the conventional multiplier approach, especially when arbitrary functions are absent from both the equation and characteristics. This method proves advantageous in handling complex multipliers and yields significant outcomes. Keywords: Lie symmetry method; the Slepyan–Palmov model; optimal system; longitudinal wave; conservation laws; homotopy operator Author: Muhammad Usman, Akhtar Hussain, F. D. Zaman, Asier Ibeas and Yahya Almalki Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Sat Nov 4 10:25:02 2023 CET ModDate: Sat Nov 4 10:32:00 2023 CET Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 13 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 1251130 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- PZNYFG+URWPalladioL-Bold Type 1 Custom yes yes no 10 0 RUUQXP+URWPalladioL-Roma Type 1 Custom yes yes no 15 0 YNVWWQ+URWPalladioL-Ital Type 1 Custom yes yes no 19 0 DVTHKG+TimesNewRomanPS-BoldItalicMT Type 1C WinAnsi yes yes no 37 0 TFRTNC+PazoMath Type 1 Builtin yes yes no 59 0 SOSTRQ+CMR10 Type 1 Builtin yes yes no 63 0 SGFOSG+PazoMath-Italic Type 1 Builtin yes yes no 67 0 XDHHRL+CMSY10 Type 1 Builtin yes yes no 71 0 LSXKAE+CMEX10 Type 1 Builtin yes yes no 75 0 QIELJB+CMMI10 Type 1 Builtin yes yes no 82 0 BJQDNG+CMBX10 Type 1 Builtin yes yes no 92 0 VPQMPJ+CMBSY10 Type 1 Builtin yes yes no 96 0 OACMZM+PazoMath-BoldItalic Type 1 Builtin yes yes no 100 0 XHCPZU+URWPalladioL-BoldItal Type 1 Custom yes yes no 104 0 TSEGZF+PazoMath-Bold Type 1 Builtin yes yes no 120 0 JEMRSF+MathematicaSans CID TrueType Identity-H yes yes yes 143 0 LFOCPI+Arial-BoldMT TrueType WinAnsi yes yes yes 150 0 SZITLF+MathematicaSans-Bold TrueType WinAnsi yes yes yes 156 0 OFVUUY+MathematicaSans-Bold CID TrueType Identity-H yes yes yes 162 0 JEMRSF+MathematicaSans CID TrueType Identity-H yes yes yes 177 0 XUPRTF+Arial-BoldMT TrueType WinAnsi yes yes yes 184 0 SZITLF+MathematicaSans-Bold TrueType WinAnsi yes yes yes 190 0 OFVUUY+MathematicaSans-Bold CID TrueType Identity-H yes yes yes 196 0 Jhove (Rel. 1.22.1, 2019-04-17) Date: 2023-11-23 02:35:40 CET RepresentationInformation: mathematics-11-04545-v2.pdf ReportingModule: PDF-hul, Rel. 1.12.1 (2019-04-17) LastModified: 2023-11-20 10:48:52 CET Size: 1251130 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 329 FreeObjects: 21 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@4d3167f4 Item: Title: Lie Group Method Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@ed9d034 Item: Title: Similarity Reductions and Invariant Solutions Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@6121c9d6 Item: Title: Local Conservation Laws via Homotopy Operator Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@87f383f Item: Title: Wave Nature of the Obtained Solutions Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@4eb7f003 Item: Title: Concluding Remarks Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@eafc191 Item: Title: References Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@612fc6eb Info: Title: Integrability Properties of the Slepyan Palmov Model Arising in the Slepyan Palmov Medium Author: Muhammad Usman, Akhtar Hussain, F. D. Zaman, Asier Ibeas and Yahya Almalki Subject: This study investigates the Slepyan Palmov (SP) model, which describes plane longitudinal waves propagating within a medium comprising a carrier medium and nonlinear oscillators. The primary objective is to analyze the integrability properties of this model. The research entails two key aspects. Firstly, the study explores the group invariant solution by utilizing reductions in symmetry subalgebras based on the optimal system. Secondly, the conservation laws are studied using the homotopy operator, which offers advantages over the conventional multiplier approach, especially when arbitrary functions are absent from both the equation and characteristics. This method proves advantageous in handling complex multipliers and yields significant outcomes. 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