Results 1 to 10 of about 23,258 (143)
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
doaj +2 more sources
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
doaj +1 more source
Journal of Mathematics, 2021 The Korteweg–de Vries (KdV) equation is a weakly nonlinear third-order differential equation which models and governs the evolution of fixed wave structures.
Tahir Ayaz +5 more
doaj +1 more source
On the rogue wave solution in the framework of a Korteweg–de Vries equation
Results in Physics, 2021 In this study, the propagation mechanism of the unstable modulated structures (e.g., rogue wave (RW)) in the framework of the family of a Korteweg–de Vries (KdV) equation is discussed.
Wedad Albalawi +2 more
doaj +1 more source
Journal of Ocean Engineering and Science, 2022 This paper studied new class of integral equation called the Korteweg-de Vries-Kadomtsev-Petviashvili (KdV-KP) equation. This equation consist of the well-known fifth-order KdV equation in the context of the Kadomtsev-Petviashvili equation.
Lanre Akinyemi +3 more
doaj +1 more source
Exact Traveling Waves of a Generalized Scale-Invariant Analogue of the Korteweg–de Vries Equation
Mathematics, 2022 In this paper, we study a generalized scale-invariant analogue of the well-known Korteweg–de Vries (KdV) equation. This generalized equation can be thought of as a bridge between the KdV equation and the SIdV equation that was discovered recently, and ...
Lewa’ Alzaleq +2 more
doaj +1 more source
New numerical solutions of fractional-order Korteweg-de Vries equation
Results in Physics, 2020 We present new solutions of fractional-order Korteweg-de Vries (KdV) equation by employing a method that utilizes advantages of both techniques of fictititous time integration and group preserving.
Mustafa Inc +3 more
doaj +1 more source
Single-Soliton Solution of KdV Equation via Hirota’s Direct Method under the Time Scale Framework
Advances in Mathematical Physics, 2022 Hirota’s direct method is one significant way to obtain solutions of soliton equations, but it is rarely studied under the time scale framework. In this paper, the generalized KdV equation on time-space scale is deduced from one newly constructed Lax ...
Yuan Kong +6 more
doaj +1 more source
The N-soliton molecule for the combined (2N+1)th-order Lax’s KdV equation
Results in Physics, 2020 Using the Hirota’s bilinear method combined with the velocity resonance mechanism, the two-soliton molecule, the three-soliton molecule and the four-soliton molecule for the third-fifth-order Lax’s KdV equation, the third-fifth-seventh-order Lax’s KdV ...
Xueping Cheng +4 more
doaj +1 more source
Supersymmetric quantum mechanics and the Korteweg-de Vries hierarchy [PDF]
, 1993 The connection between supersymmetric quantum mechanics and the Korteweg- de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws.
Grant, Aaron K., Rosner, Jonathan L.
core +2 more sources