A modified formal Lagrangian formulation for general differential equations
Abstract In this paper, we propose a modified formal Lagrangian formulation by introducing dummy dependent variables and prove the existence of such a formulation for any system of differential equations. The corresponding Euler–Lagrange equations, consisting of the original system and its adjoint s...
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Gespeichert in:
| Autor*in: |
Peng, Linyu [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Japan journal of industrial and applied mathematics - Springer Japan, 1991, 39(2022), 2 vom: 03. Feb., Seite 573-598 |
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| Übergeordnetes Werk: |
volume:39 ; year:2022 ; number:2 ; day:03 ; month:02 ; pages:573-598 |
| Links: |
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| DOI / URN: |
10.1007/s13160-022-00500-7 |
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OLC2078596817 |
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| 520 | |a Abstract In this paper, we propose a modified formal Lagrangian formulation by introducing dummy dependent variables and prove the existence of such a formulation for any system of differential equations. The corresponding Euler–Lagrange equations, consisting of the original system and its adjoint system about the dummy variables, reduce to the original system via a simple substitution for the dummy variables. The formulation is applied to study conservation laws of differential equations through Noether’s Theorem and in particular, a nontrivial conservation law of the Fornberg–Whitham equation is obtained by using its Lie point symmetries. Finally, a correspondence between conservation laws of the incompressible Euler equations and variational symmetries of the relevant modified formal Lagrangian is shown. | ||
| 650 | 4 | |a Modified formal Lagrangians | |
| 650 | 4 | |a Self-adjointness | |
| 650 | 4 | |a Symmetries | |
| 650 | 4 | |a Conservation laws | |
| 650 | 4 | |a Noether’s Theorem | |
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10.1007/s13160-022-00500-7 doi (DE-627)OLC2078596817 (DE-He213)s13160-022-00500-7-p DE-627 ger DE-627 rakwb eng 510 VZ Peng, Linyu verfasserin (orcid)0000-0002-9255-8575 aut A modified formal Lagrangian formulation for general differential equations 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2022 Abstract In this paper, we propose a modified formal Lagrangian formulation by introducing dummy dependent variables and prove the existence of such a formulation for any system of differential equations. The corresponding Euler–Lagrange equations, consisting of the original system and its adjoint system about the dummy variables, reduce to the original system via a simple substitution for the dummy variables. The formulation is applied to study conservation laws of differential equations through Noether’s Theorem and in particular, a nontrivial conservation law of the Fornberg–Whitham equation is obtained by using its Lie point symmetries. Finally, a correspondence between conservation laws of the incompressible Euler equations and variational symmetries of the relevant modified formal Lagrangian is shown. Modified formal Lagrangians Self-adjointness Symmetries Conservation laws Noether’s Theorem Enthalten in Japan journal of industrial and applied mathematics Springer Japan, 1991 39(2022), 2 vom: 03. Feb., Seite 573-598 (DE-627)131006088 (DE-600)1086800-8 (DE-576)027067874 0916-7005 nnns volume:39 year:2022 number:2 day:03 month:02 pages:573-598 https://doi.org/10.1007/s13160-022-00500-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 39 2022 2 03 02 573-598 |
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10.1007/s13160-022-00500-7 doi (DE-627)OLC2078596817 (DE-He213)s13160-022-00500-7-p DE-627 ger DE-627 rakwb eng 510 VZ Peng, Linyu verfasserin (orcid)0000-0002-9255-8575 aut A modified formal Lagrangian formulation for general differential equations 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2022 Abstract In this paper, we propose a modified formal Lagrangian formulation by introducing dummy dependent variables and prove the existence of such a formulation for any system of differential equations. The corresponding Euler–Lagrange equations, consisting of the original system and its adjoint system about the dummy variables, reduce to the original system via a simple substitution for the dummy variables. The formulation is applied to study conservation laws of differential equations through Noether’s Theorem and in particular, a nontrivial conservation law of the Fornberg–Whitham equation is obtained by using its Lie point symmetries. Finally, a correspondence between conservation laws of the incompressible Euler equations and variational symmetries of the relevant modified formal Lagrangian is shown. Modified formal Lagrangians Self-adjointness Symmetries Conservation laws Noether’s Theorem Enthalten in Japan journal of industrial and applied mathematics Springer Japan, 1991 39(2022), 2 vom: 03. Feb., Seite 573-598 (DE-627)131006088 (DE-600)1086800-8 (DE-576)027067874 0916-7005 nnns volume:39 year:2022 number:2 day:03 month:02 pages:573-598 https://doi.org/10.1007/s13160-022-00500-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 39 2022 2 03 02 573-598 |
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10.1007/s13160-022-00500-7 doi (DE-627)OLC2078596817 (DE-He213)s13160-022-00500-7-p DE-627 ger DE-627 rakwb eng 510 VZ Peng, Linyu verfasserin (orcid)0000-0002-9255-8575 aut A modified formal Lagrangian formulation for general differential equations 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2022 Abstract In this paper, we propose a modified formal Lagrangian formulation by introducing dummy dependent variables and prove the existence of such a formulation for any system of differential equations. The corresponding Euler–Lagrange equations, consisting of the original system and its adjoint system about the dummy variables, reduce to the original system via a simple substitution for the dummy variables. The formulation is applied to study conservation laws of differential equations through Noether’s Theorem and in particular, a nontrivial conservation law of the Fornberg–Whitham equation is obtained by using its Lie point symmetries. Finally, a correspondence between conservation laws of the incompressible Euler equations and variational symmetries of the relevant modified formal Lagrangian is shown. Modified formal Lagrangians Self-adjointness Symmetries Conservation laws Noether’s Theorem Enthalten in Japan journal of industrial and applied mathematics Springer Japan, 1991 39(2022), 2 vom: 03. Feb., Seite 573-598 (DE-627)131006088 (DE-600)1086800-8 (DE-576)027067874 0916-7005 nnns volume:39 year:2022 number:2 day:03 month:02 pages:573-598 https://doi.org/10.1007/s13160-022-00500-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 39 2022 2 03 02 573-598 |
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10.1007/s13160-022-00500-7 doi (DE-627)OLC2078596817 (DE-He213)s13160-022-00500-7-p DE-627 ger DE-627 rakwb eng 510 VZ Peng, Linyu verfasserin (orcid)0000-0002-9255-8575 aut A modified formal Lagrangian formulation for general differential equations 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2022 Abstract In this paper, we propose a modified formal Lagrangian formulation by introducing dummy dependent variables and prove the existence of such a formulation for any system of differential equations. The corresponding Euler–Lagrange equations, consisting of the original system and its adjoint system about the dummy variables, reduce to the original system via a simple substitution for the dummy variables. The formulation is applied to study conservation laws of differential equations through Noether’s Theorem and in particular, a nontrivial conservation law of the Fornberg–Whitham equation is obtained by using its Lie point symmetries. Finally, a correspondence between conservation laws of the incompressible Euler equations and variational symmetries of the relevant modified formal Lagrangian is shown. Modified formal Lagrangians Self-adjointness Symmetries Conservation laws Noether’s Theorem Enthalten in Japan journal of industrial and applied mathematics Springer Japan, 1991 39(2022), 2 vom: 03. Feb., Seite 573-598 (DE-627)131006088 (DE-600)1086800-8 (DE-576)027067874 0916-7005 nnns volume:39 year:2022 number:2 day:03 month:02 pages:573-598 https://doi.org/10.1007/s13160-022-00500-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 39 2022 2 03 02 573-598 |
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10.1007/s13160-022-00500-7 doi (DE-627)OLC2078596817 (DE-He213)s13160-022-00500-7-p DE-627 ger DE-627 rakwb eng 510 VZ Peng, Linyu verfasserin (orcid)0000-0002-9255-8575 aut A modified formal Lagrangian formulation for general differential equations 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2022 Abstract In this paper, we propose a modified formal Lagrangian formulation by introducing dummy dependent variables and prove the existence of such a formulation for any system of differential equations. The corresponding Euler–Lagrange equations, consisting of the original system and its adjoint system about the dummy variables, reduce to the original system via a simple substitution for the dummy variables. The formulation is applied to study conservation laws of differential equations through Noether’s Theorem and in particular, a nontrivial conservation law of the Fornberg–Whitham equation is obtained by using its Lie point symmetries. Finally, a correspondence between conservation laws of the incompressible Euler equations and variational symmetries of the relevant modified formal Lagrangian is shown. Modified formal Lagrangians Self-adjointness Symmetries Conservation laws Noether’s Theorem Enthalten in Japan journal of industrial and applied mathematics Springer Japan, 1991 39(2022), 2 vom: 03. Feb., Seite 573-598 (DE-627)131006088 (DE-600)1086800-8 (DE-576)027067874 0916-7005 nnns volume:39 year:2022 number:2 day:03 month:02 pages:573-598 https://doi.org/10.1007/s13160-022-00500-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 39 2022 2 03 02 573-598 |
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Abstract In this paper, we propose a modified formal Lagrangian formulation by introducing dummy dependent variables and prove the existence of such a formulation for any system of differential equations. The corresponding Euler–Lagrange equations, consisting of the original system and its adjoint system about the dummy variables, reduce to the original system via a simple substitution for the dummy variables. The formulation is applied to study conservation laws of differential equations through Noether’s Theorem and in particular, a nontrivial conservation law of the Fornberg–Whitham equation is obtained by using its Lie point symmetries. Finally, a correspondence between conservation laws of the incompressible Euler equations and variational symmetries of the relevant modified formal Lagrangian is shown. © The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2022 |
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Abstract In this paper, we propose a modified formal Lagrangian formulation by introducing dummy dependent variables and prove the existence of such a formulation for any system of differential equations. The corresponding Euler–Lagrange equations, consisting of the original system and its adjoint system about the dummy variables, reduce to the original system via a simple substitution for the dummy variables. The formulation is applied to study conservation laws of differential equations through Noether’s Theorem and in particular, a nontrivial conservation law of the Fornberg–Whitham equation is obtained by using its Lie point symmetries. Finally, a correspondence between conservation laws of the incompressible Euler equations and variational symmetries of the relevant modified formal Lagrangian is shown. © The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2022 |
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Abstract In this paper, we propose a modified formal Lagrangian formulation by introducing dummy dependent variables and prove the existence of such a formulation for any system of differential equations. The corresponding Euler–Lagrange equations, consisting of the original system and its adjoint system about the dummy variables, reduce to the original system via a simple substitution for the dummy variables. The formulation is applied to study conservation laws of differential equations through Noether’s Theorem and in particular, a nontrivial conservation law of the Fornberg–Whitham equation is obtained by using its Lie point symmetries. Finally, a correspondence between conservation laws of the incompressible Euler equations and variational symmetries of the relevant modified formal Lagrangian is shown. © The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2022 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2078596817</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230506013151.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">221220s2022 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s13160-022-00500-7</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2078596817</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s13160-022-00500-7-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Peng, Linyu</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0002-9255-8575</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A modified formal Lagrangian formulation for general differential equations</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2022</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, we propose a modified formal Lagrangian formulation by introducing dummy dependent variables and prove the existence of such a formulation for any system of differential equations. The corresponding Euler–Lagrange equations, consisting of the original system and its adjoint system about the dummy variables, reduce to the original system via a simple substitution for the dummy variables. The formulation is applied to study conservation laws of differential equations through Noether’s Theorem and in particular, a nontrivial conservation law of the Fornberg–Whitham equation is obtained by using its Lie point symmetries. Finally, a correspondence between conservation laws of the incompressible Euler equations and variational symmetries of the relevant modified formal Lagrangian is shown.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Modified formal Lagrangians</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Self-adjointness</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Symmetries</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Conservation laws</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Noether’s Theorem</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Japan journal of industrial and applied mathematics</subfield><subfield code="d">Springer Japan, 1991</subfield><subfield code="g">39(2022), 2 vom: 03. Feb., Seite 573-598</subfield><subfield code="w">(DE-627)131006088</subfield><subfield code="w">(DE-600)1086800-8</subfield><subfield code="w">(DE-576)027067874</subfield><subfield code="x">0916-7005</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:39</subfield><subfield code="g">year:2022</subfield><subfield code="g">number:2</subfield><subfield code="g">day:03</subfield><subfield code="g">month:02</subfield><subfield code="g">pages:573-598</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s13160-022-00500-7</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">39</subfield><subfield code="j">2022</subfield><subfield code="e">2</subfield><subfield code="b">03</subfield><subfield code="c">02</subfield><subfield code="h">573-598</subfield></datafield></record></collection>
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