Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userKdV equation beyond standard assumptions on initial data
124
0
0.0
(
0
)
Authors
Alexei Rybkin
Ask ChatGPT about the research
No Arabic abstract
We show that the Cauchy problem for the KdV equation can be solved by the inverse scattering transform (IST) for any initial data bounded from below, decaying sufficiently rapidly at plus infinity, but unrestricted otherwise. Thus our approach doesnt require any boundary condition at minus infinity.
rate research
Read More
Symmetries of a differential equations is one of the most important concepts in theory of differential equations and physics. One of the most prominent equations is KdV (Kortwege-de Vries) equation with application in shallow water theory. In this paper we are going to explain a particular method for finding symmetries of KdV equation, which is called Harrison method. Our tools in this method are Lie derivatives and differential forms, which will be discussed in the first section more precisely. In second chapter we will have some analysis on the solutions of KdV equation and we give a method, which is called first integral method for finding the solutions of KdV equation.
This paper is a continuation of arXiv:17.01.02867. We give here rigorous solution of the parametrix problem for Toda rarefaction problem and complete asymptotic analysis, justifying the asymptotics obtained in arXiv:17.01.02867.
Regarding $N$-soliton solutions, the trigonometric type, the hyperbolic type, and the exponential type solutions are well studied. While for the elliptic type solution, we know only the one-soliton solution so far. Using the commutative B{a}cklund transformation, we have succeeded in constructing the KdV static elliptic $N$-soliton solution, which means that we have constructed infinitely many solutions for the $wp$-function type differential equation.
begin{abstract} We show that if the initial profile $qleft( xright) $ for the Korteweg-de Vries (KdV) equation is essentially semibounded from below and $int^{infty }x^{5/2}leftvert qleft( xright) rightvert dx<infty,$ (no decay at $-infty$ is required) then the KdV has a unique global classical solution given by a determinant formula. This result is best known to date. end{abstract}
In this paper we show some exact solutions for the general fifth order KdV equation. These solutions are obtained by the extended tanh method.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
