Nonlocal Coupled HI-MKdV Systems

Abstract

We first study coupled Hirota-Iwao modified KdV (HI-mKdV) systems and give all possible local and nonlocal reductions of these systems. We then present Hirota bilinear forms of these systems and give one-soliton solutions of them with the help of pfaffians. By using the soliton solutions of the coupled HI-mKdV systems for $N=2,3,$ and $N=4$ we find one-soliton solutions of the local and nonlocal reduced equations.

32 pages, 14 figures

References in corpus (14)

• Nonlocal Nonlinear Schrödinger Equations and Their Soliton Solutions
• Integrable $\mathcal{P}T$-symmetric local and nonlocal vector nonlinear Schrödinger equations: a unified two-parameter model
• General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions
• Dynamics of higher-order rational solitons for the nonlocal nonlinear Schrodinger equation with the self-induced parity-time-symmetric potential
• Periodic and Hyperbolic Soliton Solutions of a Number of Nonlocal PT-Symmetric Nonlinear Equations
• Nonlocal Fordy - Kulish Equations on Symmetric Spaces
• Interplay between the Inverse Scattering Method and Fokas's Unified Transform with an Application
• On integrable wave interactions and Lax pairs on symmetric spaces
• Solutions of local and nonlocal equations reduced from the AKNS hierarchy
• On nonlocal models of Kulish-Sklyanin type and generalized Fourier transforms
• Integrable nonlocal complex mKdV equation: soliton solution and gauge equivalence
• General $N$-solitons and their dynamics in several nonlocal nonlinear Schrödinger equations
• Nonlocal Modified KdV Equations and Their Soliton Solutions
• Inverse scattering transform for the nonlocal reverse space-time Sine-Gordon, Sinh-Gordon and nonlinear Schrödinger equations with nonzero boundary conditions

Cited by in corpus (6)

• Nonlocal KdV Equations
• Discrete Symmetries and Nonlocal Reductions
• Nonlocal Hydrodynamic Type of Equations
• Soliton solutions of the shifted nonlocal NLS and MKdV equations
• Hirota bilinear forms of the AKNS($N$) systems
• $(2+1)$-dimensional AKNS($-N$) Systems: $N=3,4$