Gaussian solitary waves for argument-Schrödinger equation
•The logarithmic nonlinear Schrödinger equation has Gaussian shaped solitons.•Solitary solutions under the quadratic potential in one dimension is given.•The dispersion relation is time-dependent due to the imaginary damping potential. We present localized analytical solutions of the logarithmic non...
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| Veröffentlicht in: | Communications in nonlinear science & numerical simulation 2020-12, Vol.91, p.105449, Article 105449 |
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| container_title | Communications in nonlinear science & numerical simulation |
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| creator | Yamano, Takuya |
| description | •The logarithmic nonlinear Schrödinger equation has Gaussian shaped solitons.•Solitary solutions under the quadratic potential in one dimension is given.•The dispersion relation is time-dependent due to the imaginary damping potential.
We present localized analytical solutions of the logarithmic nonlinear Schrödinger equation, i.e., the so-called the argument-Schrödinger equation. The Gaussian solitary waveform is shown to be the solution, and we obtain the explicit form in a one-dimensional case when the dynamics evolve under a quadratic potential. The dispersion relation becomes time-dependent due to the logarithmic nonlinearity. |
| doi_str_mv | 10.1016/j.cnsns.2020.105449 |
| format | Article |
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We present localized analytical solutions of the logarithmic nonlinear Schrödinger equation, i.e., the so-called the argument-Schrödinger equation. The Gaussian solitary waveform is shown to be the solution, and we obtain the explicit form in a one-dimensional case when the dynamics evolve under a quadratic potential. The dispersion relation becomes time-dependent due to the logarithmic nonlinearity.</description><identifier>ISSN: 1007-5704</identifier><identifier>EISSN: 1878-7274</identifier><identifier>DOI: 10.1016/j.cnsns.2020.105449</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Exact solutions ; Gaussons ; Logarithmic nonlinearity ; Nonlinear equations ; Nonlinear Schrödinger equation ; Nonlinearity ; Normal distribution ; Schrodinger equation ; Solitary waves ; Waveforms</subject><ispartof>Communications in nonlinear science & numerical simulation, 2020-12, Vol.91, p.105449, Article 105449</ispartof><rights>2020 Elsevier B.V.</rights><rights>Copyright Elsevier Science Ltd. Dec 2020</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c331t-c2cef5fd05aa331b835875b5305213e23e7576efcfd74be5314c3e790293e0413</citedby><cites>FETCH-LOGICAL-c331t-c2cef5fd05aa331b835875b5305213e23e7576efcfd74be5314c3e790293e0413</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.cnsns.2020.105449$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3541,27915,27916,45986</link.rule.ids></links><search><creatorcontrib>Yamano, Takuya</creatorcontrib><title>Gaussian solitary waves for argument-Schrödinger equation</title><title>Communications in nonlinear science & numerical simulation</title><description>•The logarithmic nonlinear Schrödinger equation has Gaussian shaped solitons.•Solitary solutions under the quadratic potential in one dimension is given.•The dispersion relation is time-dependent due to the imaginary damping potential.
We present localized analytical solutions of the logarithmic nonlinear Schrödinger equation, i.e., the so-called the argument-Schrödinger equation. The Gaussian solitary waveform is shown to be the solution, and we obtain the explicit form in a one-dimensional case when the dynamics evolve under a quadratic potential. The dispersion relation becomes time-dependent due to the logarithmic nonlinearity.</description><subject>Exact solutions</subject><subject>Gaussons</subject><subject>Logarithmic nonlinearity</subject><subject>Nonlinear equations</subject><subject>Nonlinear Schrödinger equation</subject><subject>Nonlinearity</subject><subject>Normal distribution</subject><subject>Schrodinger equation</subject><subject>Solitary waves</subject><subject>Waveforms</subject><issn>1007-5704</issn><issn>1878-7274</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kE1OwzAQhS0EEqVwAjaRWKf4N06QWKAKClIlFsDacpxxcdQ6rZ0UcTEuwMVwCWtWM3p634zeQ-iS4BnBpLhuZ8ZHH2cU04MiOK-O0ISUsswllfw47RjLXEjMT9FZjC1OVCX4BN0s9BCj0z6L3dr1OnxmH3oPMbNdyHRYDRvwff5i3sP3V-P8CkIGu0H3rvPn6MTqdYSLvzlFbw_3r_PHfPm8eJrfLXPDGOlzQw1YYRsstE5CXTJRSlELhgUlDCgDKWQB1thG8hoEI9wkrcK0YoA5YVN0Nd7dhm43QOxV2w3Bp5eK8oIUpKwITi42ukzoYgxg1Ta4TcqjCFaHklSrfktSh5LUWFKibkcKUoC9g6CiceANNC6A6VXTuX_5HxrrcQ0</recordid><startdate>202012</startdate><enddate>202012</enddate><creator>Yamano, Takuya</creator><general>Elsevier B.V</general><general>Elsevier Science Ltd</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>202012</creationdate><title>Gaussian solitary waves for argument-Schrödinger equation</title><author>Yamano, Takuya</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c331t-c2cef5fd05aa331b835875b5305213e23e7576efcfd74be5314c3e790293e0413</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Exact solutions</topic><topic>Gaussons</topic><topic>Logarithmic nonlinearity</topic><topic>Nonlinear equations</topic><topic>Nonlinear Schrödinger equation</topic><topic>Nonlinearity</topic><topic>Normal distribution</topic><topic>Schrodinger equation</topic><topic>Solitary waves</topic><topic>Waveforms</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yamano, Takuya</creatorcontrib><collection>CrossRef</collection><jtitle>Communications in nonlinear science & numerical simulation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yamano, Takuya</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Gaussian solitary waves for argument-Schrödinger equation</atitle><jtitle>Communications in nonlinear science & numerical simulation</jtitle><date>2020-12</date><risdate>2020</risdate><volume>91</volume><spage>105449</spage><pages>105449-</pages><artnum>105449</artnum><issn>1007-5704</issn><eissn>1878-7274</eissn><abstract>•The logarithmic nonlinear Schrödinger equation has Gaussian shaped solitons.•Solitary solutions under the quadratic potential in one dimension is given.•The dispersion relation is time-dependent due to the imaginary damping potential.
We present localized analytical solutions of the logarithmic nonlinear Schrödinger equation, i.e., the so-called the argument-Schrödinger equation. The Gaussian solitary waveform is shown to be the solution, and we obtain the explicit form in a one-dimensional case when the dynamics evolve under a quadratic potential. The dispersion relation becomes time-dependent due to the logarithmic nonlinearity.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cnsns.2020.105449</doi></addata></record> |
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| ispartof | Communications in nonlinear science & numerical simulation, 2020-12, Vol.91, p.105449, Article 105449 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Exact solutions Gaussons Logarithmic nonlinearity Nonlinear equations Nonlinear Schrödinger equation Nonlinearity Normal distribution Schrodinger equation Solitary waves Waveforms |
| title | Gaussian solitary waves for argument-Schrödinger equation |
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