Symmetric discrete AKP and BKP equations
We show that when KP (Kadomtsev-Petviashvili) τ functions allow special symmetries, the discrete BKP equation can be expressed as a linear combination of the discrete AKP equation and its reflected symmetric forms. Thus the discrete AKP and BKP equations can share the same τ functions with these sym...
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| Veröffentlicht in: | Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2021-02, Vol.54 (7), p.75201 |
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| container_title | Journal of physics. A, Mathematical and theoretical |
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| creator | Li, Shangshuai Nijhoff, Frank W Sun, Ying-ying Zhang, Da-jun |
| description | We show that when KP (Kadomtsev-Petviashvili) τ functions allow special symmetries, the discrete BKP equation can be expressed as a linear combination of the discrete AKP equation and its reflected symmetric forms. Thus the discrete AKP and BKP equations can share the same τ functions with these symmetries. Such a connection is extended to 4 dimensional (i.e. higher order) discrete AKP and BKP equations in the corresponding discrete hierarchies. Various explicit forms of such τ functions, including Hirota's form, Gramian, Casoratian and polynomial, are given. Symmetric τ functions of Cauchy matrix form that are composed of Weierstrass σ functions are investigated. As a result we obtain a discrete BKP equation with elliptic coefficients. |
| doi_str_mv | 10.1088/1751-8121/abd998 |
| format | Article |
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Thus the discrete AKP and BKP equations can share the same τ functions with these symmetries. Such a connection is extended to 4 dimensional (i.e. higher order) discrete AKP and BKP equations in the corresponding discrete hierarchies. Various explicit forms of such τ functions, including Hirota's form, Gramian, Casoratian and polynomial, are given. Symmetric τ functions of Cauchy matrix form that are composed of Weierstrass σ functions are investigated. As a result we obtain a discrete BKP equation with elliptic coefficients.</description><identifier>ISSN: 1751-8113</identifier><identifier>EISSN: 1751-8121</identifier><identifier>DOI: 10.1088/1751-8121/abd998</identifier><identifier>CODEN: JPHAC5</identifier><language>eng</language><publisher>IOP Publishing</publisher><subject>discrete AKP ; discrete BKP ; elliptic function ; solution ; symmetric tau function</subject><ispartof>Journal of physics. 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A, Mathematical and theoretical</title><addtitle>JPhysA</addtitle><addtitle>J. Phys. A: Math. Theor</addtitle><description>We show that when KP (Kadomtsev-Petviashvili) τ functions allow special symmetries, the discrete BKP equation can be expressed as a linear combination of the discrete AKP equation and its reflected symmetric forms. Thus the discrete AKP and BKP equations can share the same τ functions with these symmetries. Such a connection is extended to 4 dimensional (i.e. higher order) discrete AKP and BKP equations in the corresponding discrete hierarchies. Various explicit forms of such τ functions, including Hirota's form, Gramian, Casoratian and polynomial, are given. Symmetric τ functions of Cauchy matrix form that are composed of Weierstrass σ functions are investigated. 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A, Mathematical and theoretical</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Shangshuai</au><au>Nijhoff, Frank W</au><au>Sun, Ying-ying</au><au>Zhang, Da-jun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Symmetric discrete AKP and BKP equations</atitle><jtitle>Journal of physics. A, Mathematical and theoretical</jtitle><stitle>JPhysA</stitle><addtitle>J. Phys. A: Math. Theor</addtitle><date>2021-02-19</date><risdate>2021</risdate><volume>54</volume><issue>7</issue><spage>75201</spage><pages>75201-</pages><issn>1751-8113</issn><eissn>1751-8121</eissn><coden>JPHAC5</coden><abstract>We show that when KP (Kadomtsev-Petviashvili) τ functions allow special symmetries, the discrete BKP equation can be expressed as a linear combination of the discrete AKP equation and its reflected symmetric forms. 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| language | eng |
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| source | Institute of Physics Journals |
| subjects | discrete AKP discrete BKP elliptic function solution symmetric tau function |
| title | Symmetric discrete AKP and BKP equations |
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