Related papers: Universal behavior of modulationally unstable medi…
An outstanding problem in Earth science is understanding the method of transport of magma in the Earth's mantle. Models for this process, transport in a viscously deformable porous media, give rise to scalar degenerate, dispersive,…
Unidirectionally coupled dynamical system is studied by focusing on the input (or boundary) dependence. Due to convective instability, noise at an up-flow is spatially amplified to form an oscillation. The response, given by the down-flow…
The interaction between two co-propagating electrostatic wavepackets characterized by arbitrary carrier wavenumber is considered. A one-dimensional (1D) non-magnetized plasma model is adopted, consisting of a cold inertial ion fluid…
The stability of colliding Bose-Einstein condensates is investigated. A set of coupled Gross-Pitaevskii equations is thus considered, and analyzed via a perturbative approach. No assumption is made on the signs (or magnitudes) of the…
We formulate and explore a generic continuum model of a polarizable active layer with neo-Hookean elasticity and chemo-mechanical interactions. Homogeneous solutions of the model equations exhibit a stationary long-wave instability when the…
We observe the breakup dynamics of an elongated cloud of condensed $^{85}$Rb atoms placed in an optical waveguide. The number of localized spatial components observed in the breakup is compared with the number of solitons predicted by a…
Stability of self-similar solutions for gravitational collapse is an important problem to be investigated from the perspectives of their nature as an attractor, critical phenomena and instability of a naked singularity. In this paper we…
Modulational instability of a uniform two-dimensional binary Bose-Einstein condensate (BEC) in the presence of quantum fluctuations is studied. The analysis is based on the coupled Gross-Pitaevskii equations. It is shown that quantum…
The modulational instability of broadband optical pulses in a four-state atomic system is investigated. In particular, starting from a recently derived generalized nonlinear Schr\"odinger equation, a wave-kinetic equation is derived. A…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at $x=\pm\infty$ to spatially periodic travelling waves. This paper is concerned with sources…
Coherent structures, such as solitary waves, appear in many physical problems, including fluid mechanics, optics, quantum physics, and plasma physics. A less studied setting is found in geophysics, where highly viscous fluids couple to…
We present an investigation of the modulational instability of partially coherent signals in electrical transmission lines. Starting from the modified Ginzburg-Landau equations and the Wigner-Moyal representation, we derive a nonlinear…
We analyze the modulational instability of nonlinear Bloch waves in topological photonic lattices. In the initial phase of the instability development captured by the linear stability analysis, long wavelength instabilities and bifurcations…
In this paper we give a frame for application of the averaging method to Bose-Einstein condensates (BECs) and obtain an abstract result upon the dynamics of BECs. Using aver- aging method, we determine the location where the modulated…
The well-known Stokes waves refer to periodic traveling waves under the gravity at the free surface of a two dimensional full water wave system. In this paper, we prove that small-amplitude Stokes waves with infinite depth are nonlinearly…
The May-Leonard model for three competing species, symmetric with respect to cyclic permutation of the variables and extended by diffusive terms, is considered. Exact time-periodic solutions of the system have been found, and their…
Unstable particles rarely feature in conjunction with integrability in 1+1D quantum field theory. However, the family of homogenous sine-Gordon models provides a rare example where both stable and unstable bound states are present in the…
Dissipationless shock waves in modulational unstable one-dimensional medium are investigated on the simplest example of integrable focusing nonlinear Schr\''odinger (NS) equation. Our approach is based on the construction of special exact…
We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of…