Related papers: Soliton dynamics for the general Degasperis-Proces…
We analyze shallow water wind waves in Currituck Sound, North Carolina and experimentally confirm, for the first time, the presence of $soliton$ $turbulence$ in ocean waves. Soliton turbulence is an exotic form of nonlinear wave motion…
We develop a computational method based on Dissipative Particle Dynamics (DPD) that introduces solvent hydrodynamic interactions to coarse-grained models of solutes, such as ions, molecules, or polymers. DPD-solvent (DPDS) is a fully…
In the multiple-soliton case, the freedom in the expansion of the solution of the perturbed KdV equation is exploited so as to transform the equation into a system of two equations: The (inte-grable) Normal Form for KdV-type solitons, which…
A simple exactly solvable kinetic model for the non-linear inelastic hard sphere Boltzmann equation is used to explore the relevance of hydrodynamics for a granular gas. The equation predicts a non-trivial homogeneous cooling state (HCS),…
Many equations that model fluid behaviour are derived from systems that encompass multiple physical forces. When the equations are written in non dimensional form appropriate to the physics of the situation, the resulting partial…
We show that the simplest universality classes of fracton hydrodynamics in more than one spatial dimension, including isotropic theories of charge and dipole conservation, can exhibit hidden "quasiconservation laws", in which certain higher…
We construct a definition of the weak solution to KdV type equations with small dispersion admitting the zero dispersion limit for soliton-like solutions. Using this definition, we obtain a system of equations (the limit problem as the…
We investigate the multi-soliton solutions to the generalized discrete KdV equation. In some cases a soliton with smaller amplitude moves faster than that with larger amplitude unlike the soliton solutions of the KdV equation. This…
A family of modified Kadomtsev-Petviashvili equations (mKP) in 2+1 dimensions is studied. This family includes the integrable mKP equation when the coefficients of the nonlinear terms and the transverse dispersion term satisfy an algebraic…
The calculation of the solvation properties of a single water molecule in liquid water is carried out in two ways. In the first, the water molecule is placed in a cavity and the solvent is treated as a dielectric continuum. This model is…
An overview is given of basic models combining discreteness in their linear parts (i.e. the models are built as dynamical lattices) and nonlinearity acting at sites of the lattices or between the sites. The considered systems include the…
In this paper we systematically derive a fourth-order continuum theory capable of reproducing mesoscale turbulence in a three-dimensional suspension of microswimmers. We start from overdamped Langevin equations for a generic microscopic…
We consider a parabolic partial differential equation that can be understood as a simple model for crowds flows. Our main assumption is that the diffusivity and the source/sink term vanish at the same point; the nonhomogeneous term is…
In classical continuum mechanics, quasi-linear systems of conservation laws can be symmetrized if they admit an additional convex conservation law. In particular, this implies the hyperbolicity of governing equations. For capillary fluids,…
Extending a previous single-temperature model, an electrostatic gyrofluid model that includes anisotropic temperatures (parallel and perpendicular) and can treat general nonlinear situations is constructed. The model is based on a…
Under certain mode-matching conditions, small-amplitude waves can be trapped by coupling to solitons of nonlinear fields. We present a model for this phenomenon, consisting of a linear equation coupled to the Korteweg-de Vries equation. The…
This paper addresses the fundamental principles of generalized Boltzmann physical kinetics, as a part of non-local physics. It is shown that the theory of transport processes (including quantum mechanics) can be considered in the frame of…
A system of first-order differential-difference equations with time lag describes the formation of density waves, called as quasi-solitons for dissipative systems in this paper. For co-moving density waves, the system reduces to some…
We consider a quasilinear KdV equation that admits compactly supported traveling wave solutions (compactons). This model is one of the most straightforward instances of degenerate dispersion, a phenomenon that appears in a variety of…
A model of nonlinear elastic medium with internal structure is considered. The medium is assumed to contain cavities, microcracks or blotches of substances that differ sharply in physical properties from the base material. To describe the…