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Sato tau functions and construction of Somos sequence

Mohamed Bensaid

Abstract

In this short article, we will reconstruct the KP equation from Plucker relations and provide some generalizations on this topic. Additionally, in the final section, we define the discrete function $τ$ in a similar manner, leading to the construction of an integer sequence that has not yet been listed in the OEIS. Furthermore, this approach allows us to construct many other sequences that are not listed in the OEIS.

Sato tau functions and construction of Somos sequence

Abstract

In this short article, we will reconstruct the KP equation from Plucker relations and provide some generalizations on this topic. Additionally, in the final section, we define the discrete function in a similar manner, leading to the construction of an integer sequence that has not yet been listed in the OEIS. Furthermore, this approach allows us to construct many other sequences that are not listed in the OEIS.
Paper Structure (9 sections, 7 theorems, 58 equations, 1 figure)

This paper contains 9 sections, 7 theorems, 58 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The standard construction of the KP equation
  3. Plücker Relation
  4. Description of the KP Equation
  5. Toda lattice
  6. The Discrete Function $\tau$
  7. Acknowledgments

Key Result

Proposition 1

The KP hierarchy equations L are equivalent to: and As a result, the compatibility condition is satisfied.

Figures (1)

  • Figure 1: Correspondence between Maya and Young

Theorems & Definitions (26)

  • Remark
  • Proposition 1
  • Example 2: Standard construction for the KP equation
  • Remark
  • Theorem 3: Sato 10
  • Proposition 4: Plücker Relation
  • proof
  • Remark
  • Definition 5: Maya Diagram
  • Proposition 6
  • ...and 16 more