Related papers: Traveling waves for SIR model on two-dimensional l…
Stability of travelling waves for the Nagumo equation on the whole line is proven using a new approach via functional inequalities and an implicitely defined phase adaption. The approach can be carried over to obtain pathwise stability of…
We prove the existence of travelling-wave solutions for a system of coupled nonlinear Schr\"{o}dinger equations arising in nonlinear optics. Such a system describes second-harmonic generation in optical materials with $\chi^{(2)}$…
In Part II of this series of papers, we consider an initial-boundary value problem for the Kolmogorov--Petrovskii--Piscounov (KPP) type equation with a discontinuous cut-off in the reaction function at concentration $u=u_c$. For fixed…
This paper is concerned with the existence and the stability of travelling wave solutions to a bistable reaction-diffusion equation with a jump discontinuious point on nonlinear term. Sub-super solution method is used throughout this paper.…
A key feature of $(1+1)$-dimensional nonlinear wave equations is that they admit left or right traveling waves, under appropriate algebraic conditions on the nonlinearities. In this paper, we prove global stability of such traveling wave…
We consider Kolmogorov--Petrovskii--Piscounov (KPP) type models in the presence of a discontinuous cut-off in reaction rate at concentration $u=u_c$. In Part I we examine permanent form travelling wave solutions (a companion paper, Part II,…
We study travelling wave solutions to Korteweg--de Vries type equations which have double power nonlinearities with integer indices, such as the Gardner equation, and fractional dispersion. Whether these equations have ground state…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…
We study the existence and stability of periodic traveling-wave solutions for complex modified Korteweg-de Vries equation. We also discuss the problem of uniform continuity of the data-solution mapping.
We use the vorticity transportation equation as the start point--with the help of stream function for two-dimensional planar incompressible flows--to obtain exact solutions that characterize evolution and dynamics of the flows. These…
In this paper, we study the solitary wave and the Cauchy problem for Half-wave-Schr\"{o}dinger equations in the plane. First, we show the existence and orbital stability of the ground states. Secondly, we prove that traveling waves exist…
In this paper, we present the two-dimensional generalized nonlinear Schr\"odinger equations with the Lax pair. These equations are related to many physical phenomena in the Bose-Einstein condensates, surface waves in deep water and…
We prove the existence of a traveling wave solution for a boundary reaction diffusion equation when the reaction term is the combustion nonlinearity with ignition temperature. A key role in the proof is plaid by an explicit formula for…
This paper is devoted to the study of traveling waves for monotone evolution systems of bistable type. Under an abstract setting, we establish the existence of bistable traveling waves for discrete and continuous-time monotone semiflows.…
We study the free boundary problem for a finite-depth layer of viscous incompressible fluid in arbitrary dimension, modeled by the Stokes or Navier-Stokes equations. In addition to the gravitational field acting in the bulk, the free…
This work deals with traveling waves in the two-dimensional Galileon theory. We use the Hirota procedure to calculate one-Galileon, two-Galileon, three-Galileon and breather-like Galileon solutions in the theory under consideration. The…
In this paper we consider traveling waves for the Gross-Pitaevskii equation which are T-periodic in each variable. We prove that if T is large enough, there exists a solution as a global minimizer of the corresponding action functional. In…
The traveling wave with the peaked profile arises in the limit of the family of traveling waves with the smooth profiles. We study the linear and nonlinear stability of the peaked traveling wave by using a local model for shallow water…
We study stability of travelling wave solutions to Korteweg--de Vries type equations which has the fractional dispersion and integer-indices double power nonlinearities. It may depend on parity combinations of the two indices and the…
This article is concerned with the existence of traveling wave solutions, including standing waves, to some models based on configurational forces, describing respectively the diffusionless phase transformations of solid materials, e.g.,…