Analytical integrability and physical solutions of d - KdV equation
A new idea of electron inertia-induced ion sound wave excitation for transonic plasma equilibrium has already been reported. In such unstable plasma equilibrium, a linear source driven Korteweg-de Vries ( d - KdV ) equation describes the nonlinear ion sound wave propagation behavior. By numerical te...
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| Veröffentlicht in: | Journal of mathematical physics 2006-03, Vol.47 (3), p.032901-032901-17 |
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| container_title | Journal of mathematical physics |
| container_volume | 47 |
| creator | Karmakar, P. K. Dwivedi, C. B. |
| description | A new idea of electron inertia-induced ion sound wave excitation for transonic plasma equilibrium has already been reported. In such unstable plasma equilibrium, a linear source driven Korteweg-de Vries
(
d
-
KdV
)
equation describes the nonlinear ion sound wave propagation behavior. By numerical techniques, two distinct classes of solution (soliton and oscillatory shocklike structures) are obtained. Present contribution deals with the systematic methodological efforts to find out its
(
d
-
KdV
)
analytical solutions. As a first step, we apply the Painleve method to test whether the derived
d
-
KdV
equation is analytically integrable or not. We find that the derived
d
-
KdV
equation is indeed analytically integrable since it satisfies Painleve property. Hirota’s bilinearization method and the modified sine-Gordon method (also termed as sine-cosine method) are used to derive the analytical results. Perturbative technique is also applied to find out quasistationary solutions. A few graphical plots are provided to offer a glimpse of the structural profiles obtained by different methods applied. It is conjectured that these solutions may open a new scope of acoustic spectroscopy in plasma hydrodynamics. |
| doi_str_mv | 10.1063/1.2173087 |
| format | Article |
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(
d
-
KdV
)
equation describes the nonlinear ion sound wave propagation behavior. By numerical techniques, two distinct classes of solution (soliton and oscillatory shocklike structures) are obtained. Present contribution deals with the systematic methodological efforts to find out its
(
d
-
KdV
)
analytical solutions. As a first step, we apply the Painleve method to test whether the derived
d
-
KdV
equation is analytically integrable or not. We find that the derived
d
-
KdV
equation is indeed analytically integrable since it satisfies Painleve property. Hirota’s bilinearization method and the modified sine-Gordon method (also termed as sine-cosine method) are used to derive the analytical results. Perturbative technique is also applied to find out quasistationary solutions. A few graphical plots are provided to offer a glimpse of the structural profiles obtained by different methods applied. It is conjectured that these solutions may open a new scope of acoustic spectroscopy in plasma hydrodynamics.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/1.2173087</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><publisher>Melville, NY: American Institute of Physics</publisher><subject>ANALYTICAL SOLUTION ; Atoms & subatomic particles ; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; ELECTRONS ; EQUILIBRIUM ; Exact sciences and technology ; EXCITATION ; HYDRODYNAMICS ; INTEGRAL CALCULUS ; ION ACOUSTIC WAVES ; KORTEWEG-DE VRIES EQUATION ; Mathematical methods in physics ; Mathematics ; MOMENT OF INERTIA ; Nonlinear equations ; NONLINEAR PROBLEMS ; Physics ; PLASMA ; Sciences and techniques of general use ; SINE-GORDON EQUATION ; SOLITONS ; SOUND WAVES ; SPECTROSCOPY</subject><ispartof>Journal of mathematical physics, 2006-03, Vol.47 (3), p.032901-032901-17</ispartof><rights>American Institute of Physics</rights><rights>2006 American Institute of Physics</rights><rights>2006 INIST-CNRS</rights><rights>Copyright American Institute of Physics Mar 2006</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c439t-1d98eee0bdd9476b145785f79167c272dd235cf01c2b43570f2838bad45caa873</citedby><cites>FETCH-LOGICAL-c439t-1d98eee0bdd9476b145785f79167c272dd235cf01c2b43570f2838bad45caa873</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jmp/article-lookup/doi/10.1063/1.2173087$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>230,314,780,784,794,885,1559,4512,27924,27925,76384,76390</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=17753080$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.osti.gov/biblio/20768741$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Karmakar, P. K.</creatorcontrib><creatorcontrib>Dwivedi, C. B.</creatorcontrib><title>Analytical integrability and physical solutions of d - KdV equation</title><title>Journal of mathematical physics</title><description>A new idea of electron inertia-induced ion sound wave excitation for transonic plasma equilibrium has already been reported. In such unstable plasma equilibrium, a linear source driven Korteweg-de Vries
(
d
-
KdV
)
equation describes the nonlinear ion sound wave propagation behavior. By numerical techniques, two distinct classes of solution (soliton and oscillatory shocklike structures) are obtained. Present contribution deals with the systematic methodological efforts to find out its
(
d
-
KdV
)
analytical solutions. As a first step, we apply the Painleve method to test whether the derived
d
-
KdV
equation is analytically integrable or not. We find that the derived
d
-
KdV
equation is indeed analytically integrable since it satisfies Painleve property. Hirota’s bilinearization method and the modified sine-Gordon method (also termed as sine-cosine method) are used to derive the analytical results. Perturbative technique is also applied to find out quasistationary solutions. A few graphical plots are provided to offer a glimpse of the structural profiles obtained by different methods applied. It is conjectured that these solutions may open a new scope of acoustic spectroscopy in plasma hydrodynamics.</description><subject>ANALYTICAL SOLUTION</subject><subject>Atoms & subatomic particles</subject><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</subject><subject>ELECTRONS</subject><subject>EQUILIBRIUM</subject><subject>Exact sciences and technology</subject><subject>EXCITATION</subject><subject>HYDRODYNAMICS</subject><subject>INTEGRAL CALCULUS</subject><subject>ION ACOUSTIC WAVES</subject><subject>KORTEWEG-DE VRIES EQUATION</subject><subject>Mathematical methods in physics</subject><subject>Mathematics</subject><subject>MOMENT OF INERTIA</subject><subject>Nonlinear equations</subject><subject>NONLINEAR PROBLEMS</subject><subject>Physics</subject><subject>PLASMA</subject><subject>Sciences and techniques of general use</subject><subject>SINE-GORDON EQUATION</subject><subject>SOLITONS</subject><subject>SOUND WAVES</subject><subject>SPECTROSCOPY</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><recordid>eNqNkE9PwyAcQInRxDk9-A0ajQdNqkBpoReTZfFfXOJFvRIK1LHUsgE16beXrYs7aTyRwOPx4wFwiuA1gkV2g64xohlkdA-MEGRlSouc7YMRhBinmDB2CI68X0CIECNkBKaTVjR9MFI0iWmD_nCiMo0JfSJalSznvd8cedt0wdjWJ7ZOVJImz-o90atOrDePwUEtGq9PtusYvN3fvU4f09nLw9N0MkslycqQIlUyrTWslCoJLSpEcsrympaooBJTrBTOcllDJHFFspzCGrOMVUKRXArBaDYG54PX-mC4lyZoOZe2bbUMHENaMEpQpM4GaunsqtM-8IXtXPyl5xjlBY7PsghdDpB01nuna7505lO4niPI1yE54tuQkb3YCoWPLWonWmn87gKleeRg5G4Hbj3ZJszv0l11_lM9Cq7-LfgL_rJuB_KlqrNvMYmhsA</recordid><startdate>20060301</startdate><enddate>20060301</enddate><creator>Karmakar, P. K.</creator><creator>Dwivedi, C. B.</creator><general>American Institute of Physics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>OTOTI</scope></search><sort><creationdate>20060301</creationdate><title>Analytical integrability and physical solutions of d - KdV equation</title><author>Karmakar, P. K. ; Dwivedi, C. B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c439t-1d98eee0bdd9476b145785f79167c272dd235cf01c2b43570f2838bad45caa873</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>ANALYTICAL SOLUTION</topic><topic>Atoms & subatomic particles</topic><topic>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</topic><topic>ELECTRONS</topic><topic>EQUILIBRIUM</topic><topic>Exact sciences and technology</topic><topic>EXCITATION</topic><topic>HYDRODYNAMICS</topic><topic>INTEGRAL CALCULUS</topic><topic>ION ACOUSTIC WAVES</topic><topic>KORTEWEG-DE VRIES EQUATION</topic><topic>Mathematical methods in physics</topic><topic>Mathematics</topic><topic>MOMENT OF INERTIA</topic><topic>Nonlinear equations</topic><topic>NONLINEAR PROBLEMS</topic><topic>Physics</topic><topic>PLASMA</topic><topic>Sciences and techniques of general use</topic><topic>SINE-GORDON EQUATION</topic><topic>SOLITONS</topic><topic>SOUND WAVES</topic><topic>SPECTROSCOPY</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Karmakar, P. K.</creatorcontrib><creatorcontrib>Dwivedi, C. B.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>OSTI.GOV</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Karmakar, P. K.</au><au>Dwivedi, C. B.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Analytical integrability and physical solutions of d - KdV equation</atitle><jtitle>Journal of mathematical physics</jtitle><date>2006-03-01</date><risdate>2006</risdate><volume>47</volume><issue>3</issue><spage>032901</spage><epage>032901-17</epage><pages>032901-032901-17</pages><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>A new idea of electron inertia-induced ion sound wave excitation for transonic plasma equilibrium has already been reported. In such unstable plasma equilibrium, a linear source driven Korteweg-de Vries
(
d
-
KdV
)
equation describes the nonlinear ion sound wave propagation behavior. By numerical techniques, two distinct classes of solution (soliton and oscillatory shocklike structures) are obtained. Present contribution deals with the systematic methodological efforts to find out its
(
d
-
KdV
)
analytical solutions. As a first step, we apply the Painleve method to test whether the derived
d
-
KdV
equation is analytically integrable or not. We find that the derived
d
-
KdV
equation is indeed analytically integrable since it satisfies Painleve property. Hirota’s bilinearization method and the modified sine-Gordon method (also termed as sine-cosine method) are used to derive the analytical results. Perturbative technique is also applied to find out quasistationary solutions. A few graphical plots are provided to offer a glimpse of the structural profiles obtained by different methods applied. It is conjectured that these solutions may open a new scope of acoustic spectroscopy in plasma hydrodynamics.</abstract><cop>Melville, NY</cop><pub>American Institute of Physics</pub><doi>10.1063/1.2173087</doi><tpages>17</tpages></addata></record> |
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| language | eng |
| recordid | cdi_crossref_primary_10_1063_1_2173087 |
| source | AIP Journals Complete; AIP Digital Archive |
| subjects | ANALYTICAL SOLUTION Atoms & subatomic particles CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ELECTRONS EQUILIBRIUM Exact sciences and technology EXCITATION HYDRODYNAMICS INTEGRAL CALCULUS ION ACOUSTIC WAVES KORTEWEG-DE VRIES EQUATION Mathematical methods in physics Mathematics MOMENT OF INERTIA Nonlinear equations NONLINEAR PROBLEMS Physics PLASMA Sciences and techniques of general use SINE-GORDON EQUATION SOLITONS SOUND WAVES SPECTROSCOPY |
| title | Analytical integrability and physical solutions of d - KdV equation |
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