Related papers: First- and second-order wave generation theory
The soliton dressing matrices for the higher-order zeros of the Riemann-Hilbert problem for the $N$-wave system are considered. For the elementary higher-order zero, i.e. whose algebraic multiplicity is arbitrary but the geometric…
This paper is devoted to the extension of the recently proposed conditional symmetry method to first order nonhomogeneous quasilinear systems which are equivalent to homogeneous systems through a locally invertible point transformation. We…
We consider a mechanism of generation of huge waves by multi-soliton resonant interactions. A non-stationary wave amplification phenomenon is found in some exact solutions of the Kadomtsev-Petviashvili (KP) equation. The mechanism proposed…
In this paper, the generalized Darboux transformation is established to the AB system, which mainly describes marginally unstable baroclinic wave packets in geophysical fluids and ultra-short pulses in nonlinear optics. We find a unified…
We propose a novel mechanism for production of baryonic asymmetry in the early Universe. The mechanism takes advantage of the strong first order phase transition that produces runaway bubbles in the hidden sector that propagate almost…
In this paper, we give the covariant formulation of second gradient electrodynamics, which is a generalized electrodynamics of second order including derivatives of higher order. The relativistic form of the field equations, the…
When traditional linearised theory is used to study gravity-capillary waves produced by flow past an obstruction, the geometry of the object is assumed to be small in one or several of its dimensions. In order to preserve the nonlinear…
A nonlinear electromagnetic scattering problem is studied in the presence of bound states in the radiation continuum. It is shown that the solution is not analytic in the nonlinear susceptibility and the conventional perturbation theory…
Nonlinear observer design for systems whose state space evolves on Lie groups is considered. The proposed method is similar to previously developed nonlinear observers in that it involves propagating the state estimate using a process model…
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…
Acoustic scattering of waves by bounded inhomogeneities in an unbounded homogeneous domain is considered. A symmetric coupled system of time-domain boundary integral equations and the second order formulation of the wave equation is…
The regions of existence are established for a class of two point nonlinear diffusion type boundary value problems (NDBVP) \begin{eqnarray*} &&\label{abst-intr-1} -s''(x)-ns'(x)-\frac{m}{x}s'(x)=f(x,s), \qquad m>0,~n\in \mathbb{R},\qquad…
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…
Extensive studies have investigated the transition mechanism of boundary layers initiated by a single primary instability. In a real-world scenario, however, multiple primary instabilities of different physical nature would coexist and…
This paper is devoted to study the existence of solutions and the monotone method of second-order periodic boundary value problems when the lower and upper solutions $\alpha$ and $\beta$ violate the boundary conditions $…
A linear theory of whistler wave is developed wihtin the paradigm of a two dimensional incompressible electron magnetohydrodynamics model. Exact analytic wave solutions are obtained for a small amplitude whistler wave that exhibit magnetic…
This paper revisits the problem of heat conduction in relativistic fluids, associated with issues concerning both stability and causality. It has long been known that the problem requires information involving second order deviations from…
Two-dimensional nonlinear gravity waves travelling in shallow water on a vertically sheared current of constant vorticity are considered. Using Euler equations, in the shallow water approximation, hyperbolic equations for the surface…
Nonlinear evolution equations of the fourth order and its partial cases are derived for describing nonlinear pressure waves in a mixture liquid and gas bubbles. Influence of viscosity and heat transfer is taken into account. Exact solutions…
We discuss a new source of gravitational waves (GWs) from first-order phase transitions. The collisions of bubbles of the new phase can efficiently produce particles that couple to the background field undergoing the transition, thereby…