KORTEWEG-de Vries equationPARTIAL differential equationsEQUATIONSPROBLEM solvingIn this paper, we explore how to generate solitary, peakon, periodic, cuspon and kink wave solution of the well-known partial differential equation Korteweg鈥揹e Vries (KdV) by using exp-function and modified exp-function...
Khare A, Cooper F (1993) One-parameter family of soliton solutions with compact support in a class of generalized Korteweg–de Vries equation. Phys Rev E 48(6):4843–4 ADSGoogle Scholar Dodan K (2005) An application for the higher order modified KdV equation by decomposition method. Commun...
Korteweg-de Vries EquationDownload Wolfram Notebook The partial differential equation (1) (Lamb 1980; Zwillinger 1997, p. 175), often abbreviated "KdV." This is a nondimensionalized version of the equation (2) derived by Korteweg and de Vries (1895) which described weakly nonlinear shall...
求解变系数KdV方程的两种方法的研究 ResearchAboutTwOMethodstoObtainSolutionsof Variable--Coefficient Korteweg・・de Vries Equations(vcKdV) ABSTRACT Inrecent years,as all important branchofthenonlinearscience soliton theory was developedrapidly and
Korteweg—de Vries (vcKdV)equation andaVariable-coemcient Kadomtsev—Pe“iashVili(vcKP)equation. The folIowing weintroducethebasiccontentsofthis paper: In chapterone,we行rst introducethe history and deVelopment ofthe soIiton, andthen by meansofseVeral exanlplesexplain three method§—-traVeIing waV...
Korteweg-de Vries equationsingular solutionCauchy problemtraveling wavenonlinear capacityHölder inequalityIn this chapter we study the local well-posedness (LWP) for the initial value problem (IVP) associated to the generalized KdV equation. We discuss the local theory for the KdV equation, the ...
In this paper, we develop an efficient structure-preserving ROMs for the Korteweg–de Vries (KdV) equation. The KdV equation is an integrable Hamiltonian PDE with a constant Poisson structure. The conserved quantities of the KdV equation are the cubic Hamiltonian (energy), quadratic momentum and ...
Stability of periodic travelling wave solutions for some classes of Korteweg-de Vries (KDV) type equationsThe following sections are included:Introduction and formulation of the main resultsSome results from the theory of elliptic functions and proof of Theorem 4.2#Introduction and formulation of the ...
We establish the nonlinear stability of solitary waves (solitons) and periodic traveling wave solutions (cnoidal waves) for a Korteweg-de Vries (KdV) equation which includes a fifth order dispersive term. The traveling wave solutions which yield solitons for zero boundary conditions and wave-trains ...
We study the convergence of higher order schemes for the Cauchy problemassociated to the KdV equation. More precisely, we design a Galerkin typeimplicit scheme which has higher order accuracy in space and first orderaccuracy in time. The convergence is established for initial data in L^2, and...