Related papers: Two Dimensional Riemann Problems for the Nonlinear…
We propose a new regularization method for constructing a shock wave type solution with nonsmooth front (interaction of shock waves) for quasilinear equations in the one-dimensional case.
We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…
In this paper, by considering the anhedral angle, we for the first time study the problem of supersonic flow of a Chaplygin gas over a conical wing with $\Lambda$-shaped cross sections, where the flow is governed by the three-dimensional…
We consider a system of two conservation laws and provide a detailed description of both classical and non-classical self-similar Riemann solutions. In particular, we demonstrate the existence of overcompressive delta shocks as singular…
General rogue waves in (1+1)-dimensional three-wave resonant interaction systems are derived by the bilinear method. These solutions are divided into three families, which correspond to a simple root, two simple roots and a double root of a…
We exploit a generic instability in the integration of steady, sonic, near-isothermal flows to find the complete transition diagram for recombination fronts (for a model system of equations). The instability requires the integration of the…
This paper studies the asymptotic stability of solution to an initial-boundary value problem for a hyperbolic-elliptic coupled system on two-dimensional half space, where the data on the boundary and at the far field are prescribed as $u_-$…
Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional defocusing nonlinear Schr\"odinger (NLS) equation. This problem is of fundamental importance as a dispersive…
We analyze the behavior of an isentropic gas in a narrow pipe with periodically-varying cross-sectional area. Using multiple-scale perturbation theory, we derive homogenized effective equations, which take the form of a constant-coefficient…
We develop a new approach and employ it to establish the global existence and nonlinear structural stability of attached weak transonic shocks in steady potential flow past three-dimensional wedges; in particular, the restriction that the…
Using numerical modeling investigated interaction of solitary waves (solitons) of the regularized long wave equation. For reception the stable model of the nonlinear medium are used methods of the linear prediction and progressive…
In this paper, we characterized resonant interaction of weakly nonlinear hyperbolic waves in gas dynamics with a real gas background. An asymptotic approach is used to study the interaction between waves, governed by the Euler equations of…
We consider an inverse problem arising in nonlinear ultrasound imaging. The propagation of ultrasound waves is modeled by a quasilinear wave equation. We make measurements at the boundary of the medium encoded in the Dirichlet-to-Neumann…
We construct a supersonic-sonic smooth patch solution for the two dimensional steady Euler equations in gas dynamics. This patch is extracted from the Frankl problem in the study of transonic flow with local supersonic bubble over an…
For a spinless quantum particle in a one-dimensional box or an electromagnetic wave in a one-dimensional cavity, the respective Dirichlet and Neumann boundary conditions both lead to non-degenerate wave functions. However, in two spatial…
We study the existence and properties of Lipschitz continuous weak solutions to the Neumann boundary value problem for a class of one-dimensional quasilinear forward-backward diffusion equations with linear convection and reaction. The…
Interchange reconnection is thought to play an important role in determining the dynamics and material composition of the slow solar wind that originates from near coronal hole boundaries. To explore the implications of this process we…
Large-time behavior of solutions to the inflow problem of full compressible Navier-Stokes equations is investigated on the half line $R^+ =(0,+\infty)$. The wave structure which contains four waves: the transonic(or degenerate) boundary…
The paper studies inverse problems of determining unknown coefficients in various semi-linear and quasi-linear wave equations. We introduce a method to solve inverse problems for non-linear equations using interaction of three waves, that…
We address ourselves to a class of systems composed of two coupled subsystems without any intra-subsystem interaction: itinerant Fermions and localized Bosons on a lattice. Switching on an interaction between the two subsystems leads to…