Breather solutions and breather-to-soliton conversions for the (2+1)-dimensional complex modified Korteweg-de Vries and Maxwell-Bloch equations
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DOI: 10.1016/j.ijleo.2020.164334
Abstract: Abstract In this paper, we will focus on the (2+1)-dimensional complex modified Korteweg-de Vries and Maxwell-Bloch (cmKdVMB) equations. According to the correlative Lax pair, the N-fold Darboux Transformations(DT) will be constructed. By virtue of the… read more here.
Keywords: modified korteweg; dimensional complex; complex modified; vries maxwell ... See more keywords
Inverse scattering transform for the coupled modified Korteweg-de Vries equation with nonzero boundary conditions
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DOI: 10.1016/j.jmaa.2021.125567
Abstract: Abstract In this paper, we study the inverse scattering transform for the coupled modified Korteweg-de Vries (cmKdV) equation with nonzero boundary conditions (NZBCs) at infinity. In order to deal with the direct and inverse scattering… read more here.
Keywords: coupled modified; modified korteweg; korteweg vries; scattering transform ... See more keywords
Genuine nonlinearity and its connection to the modified Korteweg–de Vries equation in phase dynamics
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DOI: 10.1088/1361-6544/ac337e
Abstract: The study of hyperbolic waves involves various notions which help characterise how these structures evolve. One important facet is the notion of genuine nonlinearity, namely the ability for shocks and rarefactions to form instead of… read more here.
Keywords: modified korteweg; nonlinearity; vries equation; korteweg vries ... See more keywords
Periodic solutions of the (2 + 1)-dimensional complex modified Korteweg-de Vries equation
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DOI: 10.1142/s0217984920502024
Abstract: The periodic solutions for the (2 + 1)-dimensional complex modified Korteweg–de Vries (cmKdV) equation are obtained by using the Darboux transformation (DT). Starting with a periodic seed, we get t... read more here.
Keywords: modified korteweg; periodic solutions; dimensional complex; complex modified ... See more keywords
Riemann–Hilbert problem for the generalized modified Korteweg–de Vries equation with N distinct arbitrary-order poles
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DOI: 10.1142/s021798492150233x
Abstract: In this work, the generalized modified Korteweg–de Vries (gmKdV) equation is constructed by the first time and is solved by the Riemann–Hilbert method with the zero boundary condition. In the direct scattering transform, the analytical… read more here.
Keywords: riemann hilbert; generalized modified; hilbert problem; modified korteweg ... See more keywords
Non-differentiable solutions of a family of modified Korteweg-de Vries equations within local fractional derivative
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DOI: 10.2298/tsci200201110y
Abstract: In this paper, a family of modified Korteweg-de Vries equations within local fractional derivative are constructed, and their non-differentiable solutions are dis-cussed by using several methods. read more here.
Keywords: family modified; within local; equations within; korteweg vries ... See more keywords
Breather's Properties within the Framework of the Modified Korteweg-de Vries Equation
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DOI: 10.3390/sym12040638
Abstract: We study a breather’s properties within the framework of the modified Korteweg–de Vries (mKdV) model, where cubic nonlinearity is essential. Extrema, moments, and invariants of a breather with different parameters have been analyzed. The conditions… read more here.
Keywords: properties within; modified korteweg; breather properties; within framework ... See more keywords