Coherent structure of Alice-Bob modified Korteweg de-Vries Equation

Abstract

To describe two-place events, Alice-Bob systems have been established by means of the shifted parity and delayed time reversal in Ref. [1]. In this paper, we mainly study exact solutions of the integrable Alice-Bob modified Korteweg de-Vries (AB-mKdV) system. The general Nth Darboux transformation for the AB-mKdV equation are constructed. By using the Darboux transformation, some types of shifted parity and time reversal symmetry breaking solutions including one-soliton, two-soliton and rogue wave solutions are explicitly obtained. In addition to the similar solutions of the mKdV equation (group invariant solutions), there are abundant new localized structures for the AB-mKdV systems.

19 pages; 8 Figs

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Cited by in corpus (4)

• Multi-place nonlocal systems
• Integrable nonlinear Klein-Gordon systems with $\mathcal{P}\mathcal{T}$ nonlocality and/or space-time exchange nonlocality
• A nonlocal variable coefficient modified KdV equation derived from two-layer fluid system and its exact solutions
• A nonlocal nonlinear Schrodinger equation derived from a two-layer fluid model