Letters in Mathematical Physics最新文献_第9页

Higher-order reductions of the Mikhalev system 米哈列夫系统的高阶还原

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-05-26 DOI: 10.1007/s11005-024-01811-1

E. V. Ferapontov, V. S. Novikov, I. Roustemoglou

{"title":"Higher-order reductions of the Mikhalev system","authors":"E. V. Ferapontov, V. S. Novikov, I. Roustemoglou","doi":"10.1007/s11005-024-01811-1","DOIUrl":"10.1007/s11005-024-01811-1","url":null,"abstract":"<div><p>We consider the 3D Mikhalev system, </p><div><div><span>$$ u_t=w_x, quad u_y= w_t-u w_x+w u_x, $$</span></div></div><p>which has first appeared in the context of KdV-type hierarchies. Under the reduction <span>(w=f(u))</span>, one obtains a pair of commuting first-order equations, </p><div><div><span>$$ u_t=f'u_x, quad u_y=(f'^2-uf'+f)u_x, $$</span></div></div><p>which govern simple wave solutions of the Mikhalev system. In this paper we study <i>higher-order</i> reductions of the form </p><div><div><span>$$ w=f(u)+epsilon a(u)u_x+epsilon ^2[b_1(u)u_{xx}+b_2(u)u_x^2]+cdots , $$</span></div></div><p>which turn the Mikhalev system into a pair of commuting higher-order equations. Here the terms at <span>(epsilon ^n)</span> are assumed to be differential polynomials of degree <i>n</i> in the <i>x</i>-derivatives of <i>u</i>. We will view <i>w</i> as an (infinite) formal series in the deformation parameter <span>(epsilon )</span>. It turns out that for such a reduction to be non-trivial, the function <i>f</i>(<i>u</i>) must be quadratic, <span>(f(u)=lambda u^2)</span>, furthermore, the value of the parameter <span>(lambda )</span> (which has a natural interpretation as an eigenvalue of a certain second-order operator acting on an infinite jet space), is quantised. There are only two positive allowed eigenvalues, <span>(lambda =1)</span> and <span>(lambda =3/2)</span>, as well as infinitely many negative rational eigenvalues. Two-component reductions of the Mikhalev system are also discussed. We emphasise that the existence of higher-order reductions of this kind is a reflection of <i>linear degeneracy</i> of the Mikhalev system, in particular, such reductions do not exist for most of the known 3D dispersionless integrable systems such as the dispersionless KP and Toda equations.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01811-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dimensional reduction formulae for spectral traces and Casimir energies 谱迹和卡西米尔能量的降维公式

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1007/s11005-024-01812-0

Alexander Strohmaier

引用次数: 0

Fermionic construction of the (frac{{mathbb Z}}{2})-graded meromorphic open-string vertex algebra and its ({mathbb Z}_2)-twisted module, II $$frac{mathbb Z}}{2}$$级联美态开弦顶点代数及其$${mathbb Z}_2$$扭曲模块的费米子构造, II

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1007/s11005-024-01795-y

Fei Qi

{"title":"Fermionic construction of the (frac{{mathbb Z}}{2})-graded meromorphic open-string vertex algebra and its ({mathbb Z}_2)-twisted module, II","authors":"Fei Qi","doi":"10.1007/s11005-024-01795-y","DOIUrl":"10.1007/s11005-024-01795-y","url":null,"abstract":"<div><p>This paper continues with Part I. We define the module for a <span>(frac{{mathbb Z}}{2})</span>-graded meromorphic open-string vertex algebra that is twisted by an involution and show that the axioms are sufficient to guarantee the convergence of products and iterates of any number of vertex operators. A module twisted by the parity involution is called a canonically <span>({mathbb Z}_2)</span>-twisted module. As an example, we give a fermionic construction of the canonically <span>({mathbb Z}_2)</span>-twisted module for the <span>(frac{{mathbb Z}}{2})</span>-graded meromorphic open-string vertex algebra constructed in Part I. Similar to the situation in Part I, the example is also built on a universal <span>({mathbb Z})</span>-graded non-anti-commutative Fock space where a creation operator and an annihilation operator satisfy the fermionic anti-commutativity relation, while no relations exist among the creation operators or among the zero modes. The Wick’s theorem still holds, though the actual vertex operator needs to be corrected from the naïve definition by normal ordering using the <span>(exp (Delta (x)))</span>-operator in Part I.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141101455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The spectral determinant for second-order elliptic operators on the real line 实线上二阶椭圆算子的谱行列式

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-05-23 DOI: 10.1007/s11005-024-01819-7

Pedro Freitas, Jiří Lipovský

引用次数: 0

On the Bloch eigenvalues, band functions and bands of the differential operator of odd order with the periodic matrix coefficients 关于奇阶微分算子的布洛赫特征值、带函数和带周期矩阵系数

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-05-10 DOI: 10.1007/s11005-024-01810-2

O. A. Veliev

引用次数: 0

Detecting causality with symplectic quandles 用交映准绳检测因果关系

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-05-06 DOI: 10.1007/s11005-024-01808-w

Ayush Jain

引用次数: 0

Topological twists of massive SQCD, Part I 大质量 SQCD 的拓扑扭曲，第一部分

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-05-04 DOI: 10.1007/s11005-024-01803-1

Johannes Aspman, Elias Furrer, Jan Manschot

引用次数: 0

Local scattering matrix for a degenerate avoided-crossing in the non-coupled regime 非耦合系统中退化避免交叉的局部散射矩阵

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-04-30 DOI: 10.1007/s11005-024-01807-x

Kenta Higuchi

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Correction to: Local index theorem for orbifold Riemann surfaces 更正：轨道黎曼曲面的局部指数定理

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-04-30 DOI: 10.1007/s11005-024-01809-9

Leon A. Takhtajan, Peter Zograf

引用次数: 0

Fermionic construction of the (frac{{{mathbb {Z}}}}{2})-graded meromorphic open-string vertex algebra and its ({{mathbb {Z}}}_2)-twisted module, I 费米子构造的$$frac{{mathbb {Z}}}}{2}$ -分级经变开弦顶点代数及其$${{mathbb {Z}}_2$ -扭曲模块, I

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-04-27 DOI: 10.1007/s11005-024-01794-z

Francesco Fiordalisi, Fei Qi

引用次数: 0