Scattering for the quartic generalised Korteweg–de Vries equation

Scattering for the Quartic Generalised Korteweg-de Vries Equation

We show that the quartic generalised KdV equation ut + uxxx + (u )x = 0 is globally wellposed for data in the critical (scale-invariant) space Ḣ −1/6 x (R) with small norm (and locally wellposed for large norm), improving a result of Gruenrock [8]. As an application we obtain scattering results in H x(R) ∩ Ḣ −1/6 x (R) for the radiation component of a perturbed soliton for this equation, improv...

Two Remarks on the Generalised Korteweg De-vries Equation

We make two observations concerning the generalised Korteweg de Vries equation ut + uxxx = μ(|u|u)x. Firstly we give a scaling argument that shows, roughly speaking, that any quantitative scattering result for L-critical equation (p = 5) automatically implies an analogous scattering result for the L-critical nonlinear Schrödinger equation iut+uxx = μ|u|4u. Secondly, in the defocusing case μ > 0...

On the Stability of the Orthogonally Quartic Functional Equation

The tanh method for solutions of the nonlinear modied Korteweg de Vries equation

In this paper, we have studied on the solutions of modied KdV equation andalso on the stability of them. We use the tanh method for this investigationand given solutions are good-behavior. The solution is shock wave and can beused in the physical investigations

A Paley–Wiener Theorem for Periodic Scattering with Applications to the Korteweg–de Vries Equation

Consider a one-dimensional Schrödinger operator which is a shortrange perturbation of a quasi-periodic, finite-gap operator. We give necessary and sufficient conditions on the left, right reflection coefficient such that the difference of the potentials has finite support to the left, right, respectively. Moreover, we apply these results to show a unique continuation type result for solutions o...