Oscillatory Solutions for Lattice Korteweg-de Vries-Type Equations

2018 ◽  
Vol 73 (2) ◽  
pp. 91-98
Author(s):  
Wei Feng ◽  
Song-Lin Zhao
Keyword(s):  
Vries Equation ◽  
Sylvester Equation ◽  
Matrix Approach ◽  
Cauchy Matrix ◽  
Oscillatory Solutions ◽  
Lattice Potential ◽  
De Vries

AbstractBy imposing some shift relations on r which satisfies the Sylvester equation KM+MK=rtc, oscillatory solutions are presented for some lattice Korteweg-de Vries-type equations, including the lattice potential Korteweg de-Vires equation, lattice potential modified Korteweg de-Vires equation, and lattice Schwarzian Korteweg-de Vries equation. This is done through the generalised Cauchy matrix approach.

A Discrete Negative Order Potential Korteweg–de Vries Equation

2016 ◽  
Vol 71 (12) ◽  
pp. 1151-1158 ◽  
Author(s):  
Song-lin Zhao ◽  
Ying-ying Sun
Keyword(s):  
Exact Solutions ◽  
Vries Equation ◽  
Matrix Approach ◽  
Cauchy Matrix ◽  
Negative Order ◽  
De Vries ◽  
Continuous Equation ◽  
Multisoliton Solutions ◽  
The Continuum

AbstractWe investigate a discrete negative order potential Korteweg–de Vries (npKdV) equation via the generalised Cauchy matrix approach. Solutions more than multisoliton solutions of this equation are derived by solving the determining equation set. We also show the semidiscrete equation and continuous equation together with their exact solutions by considering the continuum limits.

scholarly journals Rational solutions for three semi-discrete modified Korteweg–de Vries-type equations

2019 ◽  
Vol 33 (32) ◽  
pp. 1950399 ◽  
Author(s):  
Ying-Ying Sun ◽  
Song-Lin Zhao
Keyword(s):  
Asymptotic Analysis ◽  
Exact Solutions ◽  
Vries Equation ◽  
Rational Solutions ◽  
Lattice Potential ◽  
De Vries ◽  
Casorati Determinant

In this paper, we consider three semi-discrete modified Korteweg–de Vries type equations which are the nonlinear lumped self-dual network equation, the semi-discrete lattice potential modified Korteweg–de Vries equation and a semi-discrete modified Korteweg–de Vries equation. We derive several kinds of exact solutions, in particular rational solutions, in terms of the Casorati determinant for these three equations, respectively. For some rational solutions, we present the related asymptotic analysis to understand their dynamics better.

Integration of the nonlinear modified Korteweg-de Vries equation with a loaded term

2020 ◽  
Vol 2020 (2) ◽  
pp. 85-98
Author(s):  
A.B. Khasanov ◽  
T.J. Allanazarova
Keyword(s):  
Vries Equation ◽  
De Vries ◽  
Loaded Term

Convergence of the Rosenau-Korteweg-de Vries Equation to the Korteweg-de Vries One

2020 ◽  
Author(s):  
Giuseppe Maria Coclite ◽  
Lorenzo di Ruvo
Keyword(s):  
A Priori Estimates ◽  
Vries Equation ◽  
A Priori ◽  
Diffusion Parameter ◽  
Priori Estimates ◽  
De Vries ◽  
Wall Interactions

The Rosenau-Korteweg-de Vries equation describes the wave-wave and wave-wall interactions. In this paper, we prove that, as the diffusion parameter is near zero, it coincides with the Korteweg-de Vries equation. The proof relies on deriving suitable a priori estimates together with an application of the Aubin-Lions Lemma.

scholarly journals A flux reconstruction method for the Korteweg-de Vries equation

2021 ◽  
Vol 1978 (1) ◽  
pp. 012031
Author(s):  
Ningbo Guo ◽  
Yaming Chen ◽  
Xiaogang Deng
Keyword(s):  
Vries Equation ◽  
Flux Reconstruction ◽  
Reconstruction Method ◽  
De Vries

Abundant rogue wave solutions for the (2 + 1)-dimensional generalized Korteweg–de Vries equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Huanhuan Lu ◽  
Yufeng Zhang
Keyword(s):  
Vries Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Third Order ◽  
First Order ◽  
Wave Solutions ◽  
De Vries ◽  
Rogue Wave Solutions ◽  
Bilinear Formulation ◽  
Hirota Bilinear

AbstractIn this paper, we analyse two types of rogue wave solutions generated from two improved ansatzs, to the (2 + 1)-dimensional generalized Korteweg–de Vries equation. With symbolic computation, the first-order rogue waves, second-order rogue waves, third-order rogue waves are generated directly from the first ansatz. Based on the Hirota bilinear formulation, another type of one-rogue waves and two-rogue waves can be obtained from the second ansatz. In addition, the dynamic behaviours of obtained rogue wave solutions are illustrated graphically.

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