Related papers: On connection between the splitting parameters of …
The shape-preserving and shape-altering collisions of dark solitons are investigated in the complex modified Korteweg-de Vries equation. The obtained dark soliton solutions are classified into two distinct types, referred to as type-I and…
A new model for Korteweg and de-Vries equation (KdV) is derived. The system under study is an open channel consisting of two concentric cylinders, rotating about their vertical axis, which is tilted by slope {\tau} from the inertial…
We study the stability and dynamics of solitons in the Korteweg-de Vries (KdV) equation in the presence of noise and deterministic forcing. The noise is space-dependent and statistically translation-invariant. We show that, for small…
We study local conservation laws for evolution equations in two independent variables. In particular, we present normal forms for the equations admitting one or two low-order conservation laws. Examples include Harry Dym equation,…
Evolution of perturbed embedded solitons in the general Hamiltonian fifth-order Korteweg--de Vries (KdV) equation is studied. When an embedded soliton is perturbed, it sheds a one-directional continuous-wave radiation. It is shown that the…
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…
Nonlinear effects in the propagation of perturbations in a dusty electron-ion plasma is studied, considering fully relativistic wave motion. A multifluid model is considered for the particles, from which a KdV equation can be derived. In…
This short survey paper is concerned with a new method to prove global well-posedness results for dispersive equations below energy spaces, namely $H^{1}$ for the Schr\"odinger equation and $L^{2}$ for the KdV equation. The main ingredient…
We study the dynamics of dark solitons in an incoherently pumped exciton-polariton condensate by means of a system composed by a generalized open-dissipative Gross-Pitaevskii equation for the polaritons' wavefunction and a rate equation for…
We study existence of helical solitons in the vector modified Korteweg-de Vries (mKdV) equations, one of which is integrable, whereas another one is non-integrable. The latter one describes nonlinear waves in various physical systems,…
We study extreme wave formation for the Korteweg-de Vries equation on the torus with random initial data of average size $\epsilon$. We establish a large deviations principle for the supremum of the solution over arbitrarily long polynomial…
The propagation of small amplitude stationary profile nonlinear solitary waves in a pair plasma is investigated employing the reductive perturbation technique via well-known Korteweg de Vries (KdV) and modified KdV (mKdV) equations, we tend…
The Korteweg-de Vries equation is a fundamental nonlinear equation that describes solitons with constant velocity. On the contrary, here we show that this equation also presents accelerated wavepacket solutions. This behavior is achieved by…
Many multi-dimensional consistent discrete systems have soliton solutions with nonzero backgrounds, which brings difficulty in the investigation of integrable characteristics. In this letter we derive infinitely many conserved quantities…
This paper concerns the problem of collision of two solitons for the quartic generalized Korteweg-de Vries equation. We introduce a new framework to describe the collision in the special case where one soliton is small with respect to the…
We consider the long-time evolution of pulses in the Korteweg-de Vries equation theory for initial distributions which produce no soliton, but instead lead to the formation of a dispersive shock wave and of a rarefaction wave. An approach…
Stationary solutions on a bounded interval for an initial-boundary value problem to Korteweg--de~Vries and modified Korteweg--de~Vries equation (for the last one both in focusing and defocusing cases) are constructed. The method of the…
We study the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\epsilon^{2}u_{xxx}=0$ in a critical scaling regime where $x$ approaches the trailing edge of the region where the KdV solution shows oscillatory…
Uniform estimates for the decay structure of the $n$-soliton solution of the Korteweg-deVries equation are obtained. The KdV equation, linearized at the $n$-soliton solution is investigated in a class $\WW$ consisting of sums of travelling…
The long-time evolution of the KdV-type solitons propagating in ferromagnetic materials is considered trough a multi-time formalism, it is governed by all equations of the KdV Hierarchy. The scaling coefficients of the higher order time…