Determinant and Pfaffian solutions of soliton equations

Jonathan J C Nimmo; Junxiao Zhao

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Determinant and Pfaffian solutions of soliton equations

机译：孤子方程的行列式和Pfaffian解

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The solutions to many soliton systems have been found or reexpressed in terms of Wronskian or Grammian determinants or Pfaffians of various types. This paper gives an introduction to the techniques used to verify such solutions and reviews some of the most important results obtained in this direction over the last 30 years. It places emphasis on the universal nature of the formulae for derivatives and the identities satisfied by these objects. It contains a detailed, but not exhaustive, set of references.

机译：已经根据各种类型的Wronskian或Grammian行列式或Pfaffian找到或重新表达了许多孤子系统的解决方案。本文介绍了用于验证此类解决方案的技术，并回顾了过去30年来在该方向上获得的一些最重要的结果。它着重强调了公式的通用性质以及这些对象所满足的身份。它包含一组详细但不详尽的参考资料。

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《Physica Scripta: An International Journal for Experimental and Theoretical Physics》 |2014年第3期|共11页
作者
Jonathan J C Nimmo; Junxiao Zhao;
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正文语种 eng
中图分类物理学;
关键词
Wronskian; Grammian; Pfaffian; Hirota's method; solitons;

机译：Wronskian;Grammian;Pfaffian;Hirota方法;孤子;

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1. Determinant and Pfaffian solutions of soliton equations [J] . Jonathan J C Nimmo, Junxiao Zhao Physica Scripta: An International Journal for Experimental and Theoretical Physics . 2014,第3期

机译：孤子方程的行列式和Pfaffian解
2. Multi-soliton and Pfaffian solutions of a (2 + 1)-dimensional nonlinear evolution equation via the Jaulent-Miodek hierarchy [J] . Meng G.-Q., Gao Y.-T., Yu X., Applied mathematics and computation . 2012,第22期

机译：通过Jaulent-Miodek层次结构的（2 +1）维非线性发展方程的多孤子和Pfaffian解
3. Soliton solutions to a higher order Ito equation: Pfaffian technique [J] . Li CX, Zeng YB Physics Letters, A . 2007,第1a2期

机译：高阶Ito方程的孤子解：Pfaffian技术
4. Generalized Kaup—Kupershmidt Solitons, Static Solitons andBoundary Generated Solitons — Solutions of the KdV andHigher Order KdV Equations [C] . G.I. Burde International Conference on Numerical Analysis and Applied Mathematics . 2010

机译：广义Kaup-kupershmidt孤子，静态孤子和孤立的孤子 - KDV和高阶KDV方程的解决方案
5. Pfaffian and Wronskian solutions to generalized integrable nonlinear partial differential equations. [D] . Asaad, Magdy G. 2012

机译：广义可积非线性偏微分方程的Pfaffian和Wronskian解。
6. Bright-Dark and Multi Solitons Solutions of (3 + 1)-Dimensional Cubic-Quintic Complex Ginzburg–Landau Dynamical Equation with Applications and Stability [O] . Chen Yue, Dianchen Lu, Muhammad Arshad, 2020

机译：（3 + 1） - 二维立方 - Quid-Complex Ginzburg-Landau的亮度和多孤子解决方案具有应用和稳定性的动态方程
7. Determinants and Pfaffians : How to obtain N-soliton solutions from 2-soliton solutions (New Developments in the Research of Integrable Systems : Continuous, Discrete, Ultra-discrete) [O] . Hirota Ryogo 2003

机译：行列式和Pfaffians：如何从2-孤子解中获得N-孤子解（可积系统研究的新进展：连续，离散，超离散）

Determinant and Pfaffian solutions of soliton equations

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