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The semiclassical limit of a nonlinear focusing Schr\"odinger equation in presence of nonconstant electric and magnetic potentials V,A is studied by taking as initial datum the ground state solution of an associated autonomous elliptic…
We discuss integrable extensions of real nonlinear wave equations with multi-soliton solutions, to their bicomplex, quaternionic, coquaternionic and octonionic versions. In particular, we investigate these variants for the local and…
We obtain theoretically the phonon-polariton spectrum in nonlinear dielectric medium with the third order Kerr-type nonlinearity. We investigate the dependence of number of the polariton spectrum branches on the intensity of electromagnetic…
The full-dimensional time-dependent Schrodinger equation for the electronic dynamics of single-electron systems in intense external fields is solved directly using a discrete method. Our approach combines the finite-difference and Lagrange…
Soliton dynamics in coupled Kerr microcavities is an important aspect of frequency comb technologies, with applications in optical communication and precision metrology. We investigate a minimal system consisting of two nearly identical…
Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schr\"odinger family of…
We consider an $N$-soliton solution of the focusing nonlinear Schr\"{o}dinger equations. We give conditions for the synchronous collision of these $N$ solitons. When the solitons velocities are well separated and the solitons have equal…
We prove some multiplicity results by means of a perturbation technique in critical point theory.
We consider the stationary one dimensional Schr\"odinger-Poisson system on a bounded interval with a background potential describing a quantum well. Using a partition function which forces the particles to remain in the quantum well, the…
We obtain the most general matrix criterion for stability and instability of multi-component solitary waves considering a system of $N$ incoherently coupled nonlinear Schrodinger equations. Soliton stability is studied as a constrained…
The integrable nonlocal nonlinear Schrodinger (NNLS) equation with the self-induced parity-time-symmetric potential [Phys. Rev. Lett. 110 (2013) 064105] is investigated, which is an integrable extension of the standard NLS equation. Its…
It is shown that the collective nonlinear interactions between intense neutrino or anti-neutrino fluxes and a dense neutrino plasma are governed by a multi-dimensional coupled cubic Schr\"odinger equation in which the interaction potential…
We study the (1+1)-dimensional quasiperiodic multicolor solitons due to cascading quadratic nonlinear response in generalized one-dimensional quasiperiodic optical superlattice waveguides and show that the dynamic equations describing the…
We consider a coupled system of nonlinear Lowest Landau Level equations. We first show the existence of multi-solitons with an exponentially localised error term in space, and then we prove a uniqueness result. We also show a long time…
Nonlinear Compton scattering is calculated for the collision of an electron with a plane wave pulse. A mid infra-red (IR) peak arises in the photon spectrum due to long-range interference associated with the pulse envelope. The case of a…
We show the instability of a charged massive scalar field in bound states around Kerr-Sen black holes. By matching the near and far region solutions of the radial part in the corresponding Klein-Gordon equation, one can show that the…
Measurements of multiplicity fluctuations of identified hadrons produced in inelastic p+p interactions at 31, 40, 80, and 158~\GeVc beam momentum are presented. Three different measures of multiplicity fluctuations are used: the scaled…
We study the perturbation by a critical term and a $(p-1)$-superlinear subcritical nonlinearity of a quasilinear elliptic equation containing a singular potential. By means of variational arguments and a version of the…
Solitons are localised wave disturbances that propagate without changing shape, a result of a nonlinear interaction which compensates for wave packet dispersion. Individual solitons may collide, but a defining feature is that they pass…
We will first review known results on multi-solitons of dispersive partial differential equations, which are special solutions behaving like the sum of many weakly-interacting solitary waves. We will then describe our recent joint work with…