Related papers: Soliton Generation and Multiple Phases in Dispersi…
Linear properties of kinetic Alfv\'{e}n waves (KAWs) and kinetic slow waves (KSWs) are studied in the framework of two-fluid magnetohydrodynamics. We obtain the wave dispersion relations that are valid in a wide range of the wave frequency…
Solitons are universal nonlinear excitations that appear in settings as varied as optics, water waves, and quantum gases [1-5]. While reduced models of soliton dynamics are well established, their validity and dynamical behaviour in…
Existence and bifurcation results are derived for quasi periodic traveling waves of discrete nonlinear Schrodinger equations with nonlocal interactions and with polynomial type potentials. Variational tools are used. Several concrete…
In nonlinear physics, the interactions among solitons are well studied thanks to the multiple soliton solutions can be obtained by various effective methods. However, it is very difficult to study interactions among different types of…
In this paper, we study the formation of solitons, their propagation and collision behaviour in an integrable multicomponent (2+1)-dimensional long wave-short wave resonance interaction ($M$-LSRI) system. First, we briefly revisit our…
We investigate the quasi-integrability properties of various deformations of the Korteweg-de Vries (KdV) equation, depending on two parameters $\varepsilon_1$ and $\varepsilon_2$, which include among them the regularized long-wave (RLW) and…
Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…
Understanding, predicting, and controlling physical processes often relies on the analysis of the dynamics of partial differential equations (PDEs). In this context, the present study offers an in-depth investigation into the nonlinear…
Dispersive shock waves (DSWs) of the defocusing radial nonlinear Schr\"odinger (rNLS) equation in two spatial dimensions are studied. This equation arises naturally in Bose-Einstein condensates, water waves and nonlinear optics. A unified…
Charge density wave (CDW) formation in two-dimensional materials is governed by complex competing lattice instabilities that remain incompletely understood. Here, we investigate the structural evolution of monolayer $\mathrm{1T-VSe}_{2}$…
The aim of this work is to study asymptotically and numerically the interaction of solitons with an external forcing with variable speed using the forced modified Korteweg-de Vries equation (mKdV). We show that the asymptotic predictions…
The core focus of this research work is to obtain invariant solutions and conservation laws of the (3+1)-dimensional ZK equation, a higher-dimensional generalization of the Korteweg--de Vries (KdV) equation, which describes the phenomenon…
The nonlinear propagation of dust acoustic solitary waves (DASWs) in an unmagnetized dusty plasma consisting of negatively charged dust fluid Boltzmann distributed electrons with two different temperatures Boltzmann distributed ions with…
The basic properties of the nucleus-acoustic (NA) solitary waves (SWs) are investigated in a super-dense self-gravitating magnetized quantum plasma (SDSGMQP) system in the presence of an external magnetic field, whose constituents are the…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
The formation and propagation of small amplitude Heavy-ion-acoustic (HIA) solitary waves and double layers in an unmagnetized collisionless multi-component plasma system consisting of superthermal electrons, Boltzmann distributed light…
The dynamics of solitons of the nonlinear Schr\"odinger equation under the influence of dissipative and dispersive perturbations is investigated. In particular a coupling to a long-wave mode is considered using extended Ginzburg-Landau…
We investigated phase defects in a quasi-one-dimensional commensurate charge density wave (CDW) system, an In atomic wire array on Si(111), using low temperature scanning tunneling microscopy. The unique four-fold degeneracy of the CDW…
Discrete materials composed of masses connected by strongly nonlinear links with anomalous behavior (reduction of elastic modulus with strain) have very interesting wave dynamics. Such links may be composed of materials exhibiting…
The notion of a delta shock wave and a singular shock wave was introduced and employed by different authors, and it was shown that a large class of Riemann problems can be solved globally with these additional building blocks. The aim of…