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Alice-Bob systems, $P_s$-$T_d$-$C$ principles and multi-soliton solutions

S. Y. Lou

Abstract

To describe two-place physical problems, many possible models named Alice-Bob (AB) systems are proposed. To find and to solve these systems, the Parity (P), time reversal (T), charge conjugation (C), shifted-parity ($P_s$, parity with a shift), delayed time reversal ($T_d$, time reversal with a delay) and their possible combinations such as PT, PC, $P_sC$, $P_sT_d$ and $P_sT_dC$ etc. can be successively used. Especially, some special types of $P_s$-$T_d$-$C$ group invariant multi-soliton solutions for the KdV-KP-Toda type, mKdV-sG type, NLS type and discrete $H_1$ type AB systems are explicitly constructed.

Alice-Bob systems, $P_s$-$T_d$-$C$ principles and multi-soliton solutions

Abstract

To describe two-place physical problems, many possible models named Alice-Bob (AB) systems are proposed. To find and to solve these systems, the Parity (P), time reversal (T), charge conjugation (C), shifted-parity (, parity with a shift), delayed time reversal (, time reversal with a delay) and their possible combinations such as PT, PC, , and etc. can be successively used. Especially, some special types of -- group invariant multi-soliton solutions for the KdV-KP-Toda type, mKdV-sG type, NLS type and discrete type AB systems are explicitly constructed.

Paper Structure

This paper contains 18 sections, 157 equations.

Table of Contents

  1. Introduction
  2. AB systems
  3. AB-BA equivalence principle (AB-BA principle).
  4. AB-KdV systems
  5. AB-NLS systems
  6. AB-MKdV systems
  7. AB-sine-Gordon equation
  8. AB-KP system
  9. AB-Toda systems
  10. AB-$H_1$ systems
  11. $P_s$-$T_d$-$C$ invariant multi-soliton solutions of the AB-systems.
  12. $P_sT_d$-invariant multi-soliton solutions of the KdV-KP-Toda type AB systems
  13. $P_sT_d$-invariant multi-soliton solutions of the MKdV-sG type AB systems
  14. $P_sT_dC$-invariant and $P_sC$-invariant multi-soliton solutions of the NLS type AB systems
  15. N-soliton solutions of the defocusing AB-NLS systems
  16. ...and 3 more sections