Related papers: Integrable nonlocal complex mKdV equation: soliton…
A non-isospectral (2+1) dimensional integrable spin equation is investigated. It is shown that its geometrical and gauge equivalent counterparts is the (2+1) dimensional nonlinear Schr\"odinger equation introduced by Zakharov and studied…
In this paper, we investigate the large-order asymptotics of multi-rational solitons of the focusing complex modified Korteweg-de Vries (c-mKdV) equation with nonzero background via the Riemann-Hilbert problems. First, based on the Lax…
The N=1 supersymmetric modified Korteweg-de Vries (SmKdV) system is transformed to a system of coupled bosonic equations with the bosonization approach. The bosonized SmKdV (BSmKdV) passes the Painlev\'{e} test and allows a set of…
Novel soliton structures are constructed for the Fokas-Lenells equation. In so doing, and after discussing the stability of continuous waves, a multiple scales perturbation theory is used to reduce the equation to a Korteweg-de Vries system…
For the nonlocal Davey-Stewartson I equation, the Darboux transformation is considered and explicit expressions of the solutions are obtained. Like the nonlocal equations in 1+1 dimensions, many solutions may have singularities. However, by…
We report complex PT-symmetric multi-soliton solutions to the Korteweg de-Vries equation that asymptotically contain one-soliton solutions, with each of them possessing the same amount of finite real energy. We demonstrate how these…
We show how the inverse scattering transform can be used as a convenient tool to derive the long-time asymptotics of shock waves for the Korteweg-de Vries (KdV) equation in the soliton region. In particular, we improve the results…
We prove the nonsqueezing property of the coupled Korteweg-de Vries (KdV) equation. Relying on Gromov's nonsqueezing theorem for finite dimensional Hamiltonian systems, the argument is to approximate the solutions to the original infinite…
We investigate whether the recently proposed PT-symmetric extensions of generalized Korteweg-de Vries equations admit genuine soliton solutions besides compacton solitary waves. For models which admit stable compactons having a width which…
We investigate the integrable structure and soliton dynamics of a coupled modified Korteweg-de Vries (cmKdV) system with a real symmetric coupling matrix. We introduce a vector reformulation of Hirota's bilinear formalism in which both the…
We consider the generalized Korteweg-de Vries equation in the supercritical case, and we are interested in solutions which converge to a soliton in large time in H^1. In the subcritical case, such solutions are forced to be exactly solitons…
Interaction of two solitons of the different polarities in the framework of modified Korteweg-de Vries (mKdV) equation is studied. Three types of soliton interaction are considered: exchange and overtaking for solitons of the same polarity,…
We obtain exact periodic solutions of the positive and negative modified Kortweg-de Vries (mKdV) equations. We examine the dynamical stability of these solitary wave lattices through direct numerical simulations. While the positive mKdV…
We discuss static spherically symmetric solutions in a recently proposed non-local infrared modification of Einstein equations induced by a term $m^2g_{\mu\nu}\Box^{-1} R$, where $m$ is a mass scale. We find that, contrary to what happens…
By introducing a Miura transformation, we derive a generalized super modified Korteweg-de Vries (gsmKdV) equation from the generalized super KdV (gsKdV) equation. It is demonstrated that, while the gsKdV equation takes Kupershmidt's super…
We study the modulated Korteweg-de~Vries equation (KdV) on the circle with a time non-homogeneous modulation acting on the linear dispersion term. By adapting the normal form approach to the modulated setting, we prove sharp unconditional…
In this paper, we systematically study the integrability and data-driven solutions of the nonlocal mKdV equation. The infinite conservation laws of the nonlocal mKdV equation and the corresponding infinite conservation quantities are given…
We present a unified operator-theoretic framework for constructing deterministic KdV soliton gases and step-type KdV solutions. Starting from Dyson's determinantal formula, we obtain a broad class of reflectionless solutions and describe…
We study the dynamics of soliton solutions to the perturbed mKdV equation $\partial_t u = \partial_x(-\partial_x^2 u -2u^3) + \epsilon V u$, where $V\in \mathcal{C}^1_b(\mathbb{R})$, $0<\epsilon\ll 1$. This type of perturbation is…
We present nonlocal integrable reductions of super AKNS coupled equations. By the use of nonlocal reductions of Ablowitz and Musslimani we find new super integrable equations. In particular we introduce nonlocal super NLS equations and the…