WebWriting the Hirota-Satsuma (HS) system of equations in a symmetrical form we find its local and new nonlocal reductions. It turns out that all reductions of the HS system are Korteweg-de Vries (KdV), complex KdV, and new nonlocal KdV equations. We obtain one-soliton solutions of these KdV equations by using the method of Hirota bilinearization. WebTAŞCAN, F., & BEKIR, A. (2011). EXACT SOLUTIONS OF COUPLED KdV EQUATION DERIVED FROM THE COUPLED NLS EQUATION USING MULTIPLE SCALES METHOD. International Journal of ...

Semi-Analytic Approach to Solving Rosenau-Hyman and Korteweg …

WebApr 13, 2024 · The numerical examples of the non-homogeneous fractional Cauchy equation and three ... M. A. Taneco-Hernández, J. F. Gómez-Aguilar, On the solutions of fractional-time wave equation with ... G. Singh, P. Kumam, I. Ullah, et al., The efficient techniques for non-linear fractional view analysis of the KdV equation, Front ... WebThe KdV equation has many applications in mechanics and wave dynamics. Therefore, researchers are carrying out work to develop and analyze modified and generalized forms … chinchou gen 4 learnset

Exact solutions of (1 + 1)-dimensional integro-differential ito, kp ...

WebThe Rosenau–Hyman equation or K n,n equation is a KdV-like equation having compaction solutions. This nonlinear partial differential equation is of the form n xxx n 0 u t a u x u (1) The equation is named after Phillip Rosenau and James M. Hyman, who used it in their 1993 study of compactions. Korteweg–de Vries (KdV) equation WebThe idea of this work is to provide a pseudo-operational collocation scheme to deal with the solution of the variable-order time-space fractional KdV–Burgers–Kuramoto equation (VOSTFKBKE). Such the fractional partial differential equation (FPDE) has three characteristics of dissipation, dispersion, and instability, which make this equation is used … In mathematics, the Korteweg–De Vries (KdV) equation is a mathematical model of waves on shallow water surfaces. It is particularly notable as the prototypical example of an exactly solvable model, that is, a non-linear partial differential equation whose solutions can be exactly and precisely specified. KdV can … See more The KdV equation is a nonlinear, dispersive partial differential equation for a function $${\displaystyle \phi }$$ of two dimensionless real variables, x and t which are proportional to space and time respectively: See more Consider solutions in which a fixed wave form (given by f(X)) maintains its shape as it travels to the right at phase speed c. Such a solution is given by φ(x,t) = f(x − ct − a) = f(X). Substituting it into the KdV equation gives the ordinary differential equation See more It can be shown that any sufficiently fast decaying smooth solution will eventually split into a finite superposition of solitons travelling to the right … See more The KdV equation has several connections to physical problems. In addition to being the governing equation of the string in the Fermi–Pasta–Ulam–Tsingou problem in the continuum limit, … See more The KdV equation has infinitely many integrals of motion (Miura, Gardner & Kruskal 1968), which do not change with time. They can be given explicitly as See more The KdV equation $${\displaystyle \partial _{t}\phi =6\,\phi \,\partial _{x}\phi -\partial _{x}^{3}\phi }$$ can be reformulated … See more The history of the KdV equation started with experiments by John Scott Russell in 1834, followed by theoretical investigations by Lord Rayleigh and Joseph Boussinesq around … See more chinchou gen 6 learnset