相关论文: Equivariant Solutions to a System of Nonlinear Wav…

We study semilinear wave equations with Ginzburg-Landau type nonlinearities multiplied by a factor $\epsilon^{-2}$, where $\epsilon>0$ is a small parameter. We prove that for suitable initial data, solutions exhibit energy concentration…

We improve on recent results that establish the existence of solutions of certain semilinear wave equations possessing an interface that roughly sweeps out a timelike surface of vanishing mean curvature in Minkowski space. Compared to…

In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this equation using a geometrical framework which allows us to…

We discuss the solitary wave solutions of a particular two-component scalar field model in two-dimensional Minkowski space. These solitary waves involve one, two or four lumps of energy. The adiabatic motion of these composite non-linear…

We consider the wave equation $\varepsilon^2(-\partial_t^2 + \Delta)u + f(u) = 0$ for $0<\varepsilon\ll 1$, where $f$ is the derivative of a balanced, double-well potential, the model case being $f(u) = u-u^3$. For equations of this form,…

We consider longwave mode of the interface instability in the system comprising of two immiscible fluid layers. The fluids fill out plane horizontal cavity which is subjected to horizontal harmonic vibration. The analysis is performed…

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…

A method for solving a quasilinear nonelliptical equation of the second order is developed and we give classification and parametrization of simple elements of the equation.We find exact solutions of an equation for potential stationary…

We provide a definitive treatment, including sharp decay and the precise late-time asymptotic profile, for generic solutions of linear wave equations with a (singular) inverse-square potential in (3+1)-dimensional Minkowski spacetime. Such…

In this paper we deal with the exterior problem for a system of nonlinear wave equations in two space dimensions, assuming that the initial data is small and smooth. We establish the same type of lower bound of the lifespan for the problem…

In this paper, it is shown how a combination of approximate symmetries of a nonlinear wave equation with small dissipations and singularity analysis provides exact analytic solutions. We perform the analysis using the Lie symmetry algebra…

We study a semilinear wave inequality with double damping on a complete noncompact Riemannian manifold. The considered problem involves a potential function $V$ depending on the space variable in front of the power nonlinearity and an…

We introduce a new class of piece-wise quadratic potentials for nonlinear wave equations with a kink solutions. The potentials allow an exact description of the spectral properties for the linearized equation at the kink. This description…

The generalized equation for the study of two-component nonlinear waves in different fields of physics is considered. In special cases, this equation is reduced to a set of the various well-known equations describing nonlinear solitary…

We construct oscillatory solutions of fully semilinear wave equations in Minkowski space satisfying a null condition of the form $$\square u:=(-\partial_{x_0}^2 +\sum_{j=1}^n \partial_{x_j}^2 )u=…

We are interested in coupled semi-linear wave equations satisfying the null condition in two space dimensions, a basic model in nonlinear wave equations. Our aim is to establish global existence of smooth solutions to this system with large…

Rotating waves are a fascinating feature of a wide array of complex systems, particularly those arising in the study of many chemical and biological processes. With many rigorous mathematical investigations of rotating waves relying on the…

We derive a novel two-component generalization of the nonlinear variational wave equation as a model for the director field of a nematic liquid crystal with a variable order parameter. The two-component nonlinear variational wave equation…

We consider a system of coupled nonlinear Schr{\"o}dinger equations in one space dimension. First, we prove the existence of multi-speed solitary waves, i.e solutions to the system with each component behaving at large times as a solitary…

In the present paper we consider a general family of two dimensional wave equations which represents a great variety of linear and nonlinear equations within the framework of the transformations of equivalence groups. We have investigated…