Pattern Formation and Solitons
In this paper, we study the smooth transition from solitons to solitary waves in localization, relation between energy and velocity, propagation and scattering property in the Fermi-Pasta-Ulam lattice analytically and numerically. A soliton…
A multiple scale model of the nonlinearly coupled KdV equations is established to predict mechanism of interaction of equatorial Rossby waves and barotropic waves in certain case. Analytically, predicted precursor radiation is a…
This paper presents new findings concerning the dynamics of the slow height variations in surfaces produced by the two-dimensional isotropic Kuramoto-Sivashinsky equation with an additional nonlinear term. In addition to the disordered…
We explore dynamics of discrete breathers and multi-breathers in finite one-dimensional chain. The model involves parabolic on-site potential with rigid constraints and linear nearest-neighbor coupling. The rigid non-ideal impact…
We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity promoting…
A system of two Schnakenberg-like reaction-diffusion equations is investigated analytically and numerically. The system has previously been used as a minimal model for concentrations of GTPases involved in the process of cell polarisation.…
We study the dynamics of superposed nonlinear waves in coherently coupled Gross-Pitaevskii (CCGP) equations with constant (autonomous system) and time varying (non-autonomous system) nonlinearity co-efficients. By employing a linear…
We discuss the behavior of solitary wave solutions of the nonlinear Schr{\"o}dinger equation (NLSE) as they interact with complex potentials, using a four parameter variational approximation based on a dissipation functional formulation of…
In this work, we study the pattern solutions of doubly nonlocal logistic map that include spatial kernels in both growth and competition terms. We show that this map includes as a particular case the nonlocal Fisher-Kolmogorov equation, and…
It is shown that the unstable evolutions of the Hermite-Gauss-type stationary solutions for the nonlocal nonlinear Schrodinger equation with the exponential-decay response function can evolve into chaotic states. This new kind of entities…
A nonlinearly generalized Camassa-Holm equation, depending an arbitrary nonlinearity power $p \neq 0$, is considered. This equation reduces to the Camassa-Holm equation when $p=1$ and shares one of the Hamiltonian structures of the…
The dune skeleton model is a reduced model to describe the formation process and dynamics of characteristic types of dunes emerging under unidirectional steady wind. Using this model, we study the dependency of the morphodynamics of…
A bifurcation analysis of dune shape transition is made. By use of a reduced model of dune morphodynamics, dune skeleton model, we elucidate the transition mechanism between different shapes of dunes under unidirectional wind. It was found…
We study stability and dynamics of the single cylindrically symmetric solitary structures and dipolar solitonic molecules in spatially nonlocal media. The main properties of the solitons, vortex solitons, and dipolar solitons are…
We study the dynamics of moving discrete breathers in an interfaced piecewise DNA molecule. This is a DNA chain in which all the base pairs are identical and there exists an interface such that the base pairs dipole moments at each side are…
The origin of 1D spirals or antisymmetric 1D pulses is explaind so far on the basis of multistability of spatially inhomogeneous and temporally oscillatory phases and so called nonvariational effects. Thus, coupled amplitude equations which…
We report observations of stable, localized, line-like structures in the spatially periodic pattern formed by nematic electroconvection, along which the phase of the pattern jumps by $\pi$. With increasing electric voltage, these lines form…
We derive the multi-field, micropolar-type continuum theory for the two-dimensional model of crystal having finite-size particles. Continuum theories are usually valid for waves with wavelength much larger than the size of primitive cell of…
We present an evaporation experiment in a single fluid layer. When latent heat associated to the evaporation is large enough, the heat flow through the free surface of the layer generates temperature gradients that can destabilize the…
The interaction of nonlinear Schr\"{o}dinger (NLS) solitons with potential wells with variable shapes is investigated numerically. For fixed initial velocities below the threshold for transmission, the outcome pattern as a function of the…