Analysis of a Chebyshev-type spectral method for the Korteweg-de Vries equation in the real line
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DOI: 10.1007/s13370-018-0635-8
Abstract: Many problems in science and engineering involve nonlinear PDEs which are posed on the real line ($${\mathbb {R}}$$R). Particular examples include a number of important nonlinear wave equations. A rigorous numerical analysis of such problems… read more here.
Keywords: chebyshev type; spectral method; vries equation; korteweg vries ... See more keywords
General lump solutions, lumpoff solutions, and rogue wave solutions with predictability for the (2+1)-dimensional Korteweg-de Vries equation
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DOI: 10.1007/s40314-019-0938-x
Abstract: In this work, the (2+1)-dimensional Korteweg-de Vries equation is investigated, which can be used to represent the amplitude of the shallow–water waves in fluids or electrostatic wave potential in plasmas. By employing the properties of… read more here.
Keywords: lumpoff solutions; dimensional korteweg; korteweg vries; vries equation ... See more keywords
Interactions between exotic multi-valued solitons of the (2+1)-dimensional Korteweg-de Vries equation describing shallow water wave
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DOI: 10.1016/j.apm.2019.11.056
Abstract: Abstract Korteweg-de Vries equation governs the weakly nonlinear long wave whose phase speed reaches a simple maximum of wave with the infinite length in shallow water wave. The exponential-form variable separation solution of (2+1)-dimensional Kortweg-de… read more here.
Keywords: korteweg vries; vries equation; multi valued; valued solitons ... See more keywords
Lump and Interaction solutions of a geophysical Korteweg–de Vries equation
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DOI: 10.1016/j.rinp.2020.103661
Abstract: Abstract This manuscript retrieve lump soliton solution for geophysical Korteweg–de Vries equation (GKdVE) with the help of Hirota bilinear method (HBM). We will also obtain lump–kink soliton (which is interaction of lump with one kink… read more here.
Keywords: lump; vries equation; korteweg vries; interaction ... See more keywords
Nonautonomous solitons for an extended forced Korteweg-de Vries equation with variable coefficients in the fluid or plasma
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DOI: 10.1080/17455030.2017.1356944
Abstract: Abstract Under investigation in this paper is an extended forced Korteweg-de Vries equation with variable coefficients in the fluid or plasma. Lax pair, bilinear forms, and bilinear Bäcklund transformations are derived. Based on the bilinear… read more here.
Keywords: equation variable; variable coefficients; extended forced; vries equation ... 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
Reply to "Comment on 'Shallow-water soliton dynamics beyond the Korteweg-de Vries equation' ".
Sign Up to like & getrecommendations! Published in 2020 at "Physical Review E"
DOI: 10.1103/physreve.101.036202
Abstract: We agree with the objection raised by Burde that the wave equation in our previous paper [Phys. Rev. E 90, 012907 (2014)PLEEE81539-375510.1103/PhysRevE.90.012907] was not derived in a consistent way. However, our paper contains an important… read more here.
Keywords: comment shallow; soliton; reply comment; korteweg vries ... See more keywords
Controllability Problems for the Korteweg–de Vries Equation with Integral Overdetermination
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DOI: 10.1134/s0012266119010130
Abstract: We establish results on the unique solvability of control problems for the Korteweg–de Vries equation and its linearized analog in a bounded domain under an integral overdetermination condition. For the Korteweg–de Vries equation itself, we… read more here.
Keywords: vries equation; problems korteweg; korteweg vries; controllability problems ... See more keywords
Rapidly oscillating solutions of a generalized Korteweg–de Vries equation
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DOI: 10.1134/s0965542517110082
Abstract: For a generalized Korteweg–de Vries equation, the existence of families of rapidly oscillating periodic solutions is proved and their asymptotic representation is found. The asymptotics of tori of different dimensions are examined. Formulas for solutions… read more here.
Keywords: generalized korteweg; solutions generalized; rapidly oscillating; korteweg vries ... See more keywords
A nonhomogeneous boundary-value problem for the 5-th Korteweg–de Vries equation posed on the half line
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DOI: 10.1216/rmj.2021.51.621
Abstract: We study the well-posedness of the 5-th Korteweg–de Vries (KdV) equation in the space H2+s(0,r) when the initial data is drawn from H2+s(0,r) and the boundary data (h1(t),h2(t),…,h5(t)) lies in the product space Hs1(0,T),…,Hs5(0,T) for… read more here.
Keywords: nonhomogeneous boundary; value problem; boundary value; korteweg vries ... See more keywords