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 ($P_s$, parity with a shift), delayed time reversal ($T_d$, time reversal with a delay) and their possible combinations such as PT, PC, $P_{s}C$, $P_s{T}_d$ and $P_s{T}_{d}C$ 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.

22 pages

References in corpus (3)

• Alice-Bob Physics: Coherent Solutions of Nonlocal KdV Systems
• Exact $P_s{T}_d$ Invariant and $P_s{T}_d$ Symmetric Breaking solutions, Symmetry Reductions and Bäcklund Transformations For An AB-KdV System
• Alice-Bob Peakon Systems

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• Curved wedges in the long-time asymptotics for the integrable nonlocal nonlinear Schrödinger equation
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• Searching for missing D'Alembert waves in nonlinear system: Nizhnik-Novikov-Veselov equation
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• Stability in integrable nonlocal nonlinear equations
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