Related papers: On the precise cusped behaviour of extreme solutio…
We consider the asymptotic behavior of solutions to the Cauchy problem for a dispersive-dissipative equation with a cubic nonlinearity. It is known that the leading term of the asymptotic profile for the solution to this problem is the…
This work is dedicated to putting on a solid analytic ground the theory of local well-posedness for the two dimensional Dysthe equation. This equation can be derived from the incompressible Navier-Stokes equation after performing an…
As mentioned by Schwartz (1974) and Cokelet (1977), it was failed to gain convergent results of limiting Stokes' waves in extremely shallow water by means of perturbation methods even with the aid of extrapolation techniques such as…
This paper is dedicated to the investigation of the asymptotic behavior of a delayed wave equation without the presence of any position term. First, it is shown that the problem is well-posed in the sense of semigroups theory. Thereafter,…
The existence of periodic waves propagating downstream on the surface of a two-dimensional infinitely deep water under gravity is established for a general class of vorticities. When reformulated as an elliptic boundary value problem in a…
A family of higher-order rational lumps on non-zero constant background of Davey-Stewartson (DS) II equation are investigated. These solutions have multiple peaks whose heights and trajectories are approximately given by asymptotical…
We study the large-time asymptotic behavior of solutions toward the combination of a viscous contact wave with two rarefaction waves for the compressible non-isentropic Navier-Stokes equations coupling with the Maxwell equations through the…
We derive precise late-time asymptotics for solutions to the wave equation on spherically symmetric, stationary and asymptotically flat spacetimes including as special cases the Schwarzschild and Reissner-Nordstrom families of black holes.…
We construct a time-asymptotic expansion with pointwise remainder estimates for solutions to 1D compressible Navier--Stokes equations. The leading-order term is the well-known diffusion wave and the higher-order terms are newly introduced…
We consider the Cauchy problem in ${\bf R}^{n}$ for strongly damped wave equations. We derive asymptotic profiles of these solutions with weighted $L^{1,1}({\bf R}^{n})$ data by using a method introduced in [10].
Results of investigation of the asymptotic behavior of solutions to the Cauchy problems for a quasi-linear parabolic equation with a small parameter at a higher derivative near singular points of limit solutions are presented. Interest to…
The rigorous asymptotic analysis for the Riemann problem of the defocusing nonlinear Schr\"{o}dinger hydrodynamics is a very interesting problem with many challenges. To date, the full analysis of this problem remains open. In this work,…
This paper is concerned with decay and symmetry properties of solitary wave solutions to a nonlocal shallow water wave model. It is shown that all supercritical solitary wave solutions are symmetric and monotone on either side of the crest.…
We bring new results in the study the asymptotic behavior of shrinking vortex pairs obtained by maximization of the kinetic energy in a 2-dimensional lake over a class of rearrangements. After improving recent results obtained for the first…
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…
Asymptotic formula is derived for the behavior of the fundamental solution of the second-order elliptic self-adjoint operator with a piecewise-smooth coefficient in front of the senior derivatives near the discontinuity surface of the…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
We consider the asymptotic behavior of solutions to nonlinear partial differential equations in the limit of short wavelength. For initial data which cause focusing at one point, we highlight critical indexes as far as the influence of the…
Solitons and cavitons (localized solutions with singularities) for the nonlocal Whitham equations are studied. The equation of a fourth order with a parameter in front of fourth derivative for traveling waves is reduced to a reversible…
We study the asymptotic behavior of solutions to the steady Navier-Stokes equations outside of an infinite cylinder in $\mathbb{R}^3$. We assume that the flow is periodic in $x_3$-direction and has no swirl. This problem is closely related…