Related papers: KdV breathers on a cnoidal wave background
We consider the extended Korteweg-de Vries (eKdV) equation as a model for long moderately nonlinear surface water waves. In the slow time formulation this equation generates fast propagating resonant radiation due to the non-convexity of…
A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type…
On the basis of relationship between the kinetic equation for two soliton clouds in the theory of the Korteweg-de Vries equation and equations of the Chaplygin gas dynamics it is shown that the existence of waves propagating without a…
We study the spectral and orbital stability of elliptic function solutions for the focusing modified Korteweg-de Vries (mKdV) equation and construct the corresponding breather solutions to exhibit the stable or unstable dynamic behavior.…
We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient…
The nonlinear Schrodinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas. However, due to the difficulty of solving this equation, in particular in high…
We present exact N-soliton optical pulses riding on a continuous-wave (c.w.) beam that propagate through and interact with a two-level active optical medium. Their representation is derived via an appropriate generalization of the inverse…
We study the periodic Schr\"odinger-Korteweg de Vries system. We describe the two-parametetric family of $2T$ periodic traveling waves of dnoidal type. The main objective of the paper is to establish their spectral stability with respect to…
We consider a randomly perturbed Korteweg-de Vries equation. The perturbation is a random potential depending both on space and time, with a white noise behavior in time, and a regular, but stationary behavior in space. We investigate the…
A technique for obtaining an approximate breather solution of the Klein-Gordon equation is presented. A breather solution of the equation describing the propagation of nonlinear waves in a graphene-based superlattice is investigated.
Solitons are non-dispersive wave solutions that arise in a diverse range of nonlinear systems, stablised by a focussing or defocussing nonlinearity. First observed in shallow water, solitons have subsequently been studied in many other…
We show that breather solutions of the Gardner equation, a natural generalization of the KdV and mKdV equations, are $H^2(\mathbb{R})$ stable. Through a variational approach, we characterize Gardner breathers as minimizers of a new Lyapunov…
The soliton resolution for the focusing modified Korteweg-de vries (mKdV) equation is established for initial conditions in some weighted Sobolev spaces. Our approach is based on the nonlinear steepest descent method and its reformulation…
We study dynamics of dark solitons in the theory of the DNLS equation by the method based on imposing the condition that this dynamics must be Hamiltonian. Combining this condition with Stokes' remark that relationships for harmonic linear…
Within the (2 + 1)-dimensional Korteweg-de Vries equation framework, new bilinear Backlund transformation and Lax pair are presented based on the binary Bell polynomials and gauge transformation. By introducing an arbitrary function, a…
We generalize the approach first proposed by Manton [Nuc. Phys. B {\bf 150}, 397 (1979)] to compute solitary wave interactions in translationally invariant, dispersive equations that support such localized solutions. The approach is…
Families of soliton pairs, namely vector solitons, are found within the context of a coupled nonlocal nonlinear Schrodinger system of equations, as appropriate for modeling beam propagation in nematic liquid crystals. In the focusing case,…
The universal theory of weakly nonlinear wave packets given by the nonlinear Schr\"odinger equation is revisited. In the limit where the group and phase velocities are very close together, a multiple scale analysis carried out beyond all…
We solve the direct scattering problem for the ultradiscrete Korteweg de Vries (udKdV) equation, over $\mathbb R$ for any potential with compact (finite) support, by explicitly constructing bound state and non-bound state eigenfunctions. We…
We mainly investigate a coupled system of the generalized nonlinear Schr\"odinger equation and the Maxwell-Bloch equations which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order effects including the…