| Citation: |
Tong Zhou. INTEGRABILITY, MATRIX EXACT SOLUTIONS AND DYNAMIC PROPERTIES FOR THE NONLOCAL MATRIX REVERSE SPACE-TIME MODIFIED KORTEWEG-DE VRIES EQUATION[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 1951-1962. doi: 10.11948/20250190
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INTEGRABILITY, MATRIX EXACT SOLUTIONS AND DYNAMIC PROPERTIES FOR THE NONLOCAL MATRIX REVERSE SPACE-TIME MODIFIED KORTEWEG-DE VRIES EQUATION
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Abstract
In this work, the nonlocal reverse space-time matrix version and its corresponding linear spectral problem are introduced from the well-known nonlocal reverse space-time modified Korteweg-de Vries (nmKdV) equation, and the integrability in the sense of infinitely many conservation laws is confirmed. The Darboux transformation for this nonlocal matrix integrable equation is constructed and proved, and several types of exact matrix solutions such as standard soliton solution, kink solution, singular periodic solution, rational solution, non-singular periodic solution, etc., are studied by taking different groups of seed solutions and spectral parameters. Furthermore, we investigate the dynamical properties of these matrix exact solutions.
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References
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Tong Zhou. INTEGRABILITY, MATRIX EXACT SOLUTIONS AND DYNAMIC PROPERTIES FOR THE NONLOCAL MATRIX REVERSE SPACE-TIME MODIFIED KORTEWEG-DE VRIES EQUATION[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 1951-1962. doi: 10.11948/20250190
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Figure 1.
Profiles of
$ |\widetilde{p}| $ $ \lambda_{1}=-0.1+0.4i $ $ \lambda_{2}=0.1+0.4i $ $ \delta^{(1)}_{11}=\delta^{(1)}_{21}=5 $ $ \delta^{(2)}_{11}=-\delta^{(2)}_{21}=-1 $ $ \lambda_{1}=0.7 $ $ \lambda_{2}=0 $ $ \delta^{(1)}_{11}=\delta^{(1)}_{21}=5 $ $ \delta^{(2)}_{11}=-\delta^{(2)}_{21}=-1 $ $ \lambda_{1}=-0.1+0.4i $ $ \lambda_{2}=0 $ $ \delta^{(1)}_{11}=\delta^{(1)}_{21}=5 $ $ \delta^{(2)}_{11}=-\delta^{(2)}_{21}=-1 $ -
Figure 2.
Profiles of
$ |\widetilde{p}| $ $ m=0 $ $ \lambda_{1}=-0.5i $ $ \alpha=0.3 $ $ \beta=0.4 $ $ m=i $ $ \lambda_{1}=1.4+0.5i $ $ \alpha=\beta=-0.99i $ -
Figure 3.
Profiles of
$ |\widetilde{p}| $ $ a_{\pm}=b_{\pm}=0 $ $ \alpha=0.1 $ $ \beta=0.5 $ $ m=0.15i $ $ \lambda_{1}=0.25i $ $ a_{\pm}=b_{\pm}=0 $ $ \alpha=0.1 $ $ \beta=0.5 $ $ m=0.07+0.18i $ $ \lambda_{1}=0.25i $