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Lie symmetry analysis and explicit solutions of the time fractional fifth-order KdV equation. [PDF]
PLoS ONE, 2014 In this paper, using the Lie group analysis method, we study the invariance properties of the time fractional fifth-order KdV equation. A systematic research to derive Lie point symmetries to time fractional fifth-order KdV equation is performed.
Gang Wei Wang, Tian Zhou Xu, Tao Feng
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Results in Physics, 2021 In this article, we study the nonlinear higher order of extended KdV equation with free surface displacement. The modified exponential rational function method is used in order to find exact solutions of the extended KdV equation.
Ali Althobaiti +3 more
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A polynomial conjecture connected with rogue waves in the KdV equation
Partial Differential Equations in Applied Mathematics, 2021 A polynomial conjecture, associated with rational solutions including rogue wave solutions of the KdV equation, is presented. The conjecture can be used to show that for the bilinear KdV equation, an arbitrary linear combination of two Wronskian ...
Wen-Xiu Ma
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On rational similarity solutions of $KdV$ and $m$-$KdV$ equations [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1983 This note presents rational similarity solutions \(u_ n\) in series for the KdV equation and \(v_ n\) for the modified-KdV equation. These solutions were expressed in terms of polynomials originally introduced by Yablonskij (1959) and Vorobiev (1965) to describe rational solutions of the second Painlevé equation.
Yoshinori Kametaka
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Lie symmetry based-analytical and numerical approach for modified Burgers-KdV equation
Results in Physics, 2018 In this work, the variable-coefficient modified Burgers-KdV equation, which arises in modeling various physical phenomena, is studied for exact and numerical solution based on Lie symmetry.
Vikas Kumar +3 more
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Complexity, 2018 The study of ion-acoustic solitary waves in a magnetized plasma has long been considered to be an important research subject and plays an increasingly important role in scientific research. Previous studies have focused on the integer-order models of ion-
Min Guo +4 more
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New lower bounds on the radius of spatial analyticity for the KdV equation [PDF]
Journal of Differential Equations, 2018 The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than $t^{-1/4}$ as time $t$ goes to infinity.
Jianhua Huang, Ming Wang
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Electronic Journal of Applied Mathematics, 2023 New solitary wave solutions for the Korteweg-de Vries (KdV) equation by a new version of the trial equation method are attained. Proper transformation reduces the Korteweg-de Vries (KdV) equation to a quadratic ordinary differential equation that is ...
Y. Pandır, A. Ekin
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Soliton-like Solutions of General Variable Coefficient Cylindrical/Spherical KdV Equation
Mathematics, 2022 The general variable coefficient cylindrical/spherical KdV equation has been investigated by using the simplified homogeneous balance method. It has been proven that if its coefficients satisfy certain constraint conditions, then the cylindrical ...
Lingxiao Li, Mingliang Wang
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