Related papers: Conditional Symmetry and Reductions for the Two-Di…
Spectral method related to Lame equation with finite-gap potential is used to study the optical cascading equations. These equations are known not to be integrable by inverse scattering method. Due to "partial integrability" two-gap…
We consider wave models with lower order terms and recollect some recent results on energy and dispersive estimates for their solution based on symbolic type estimates for coefficients and partly stabilisation conditions. The exposition is…
In this paper, we study the indirect stabilization problem for a system of two coupled semilinear wave equations with internal damping in a bounded domain in $\mathbb{R}^3$. The nonlinearity is assumed to be subcritical, defocusing and…
This paper deals with a one-dimensional wave equation with a nonlinear dynamic boundary condition and a Neumann-type boundary control acting on the other extremity. We consider a class of nonlinear stabilizing feedbacks that only depend on…
We present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, we show that the system of perturbative…
In this paper we will develop linear and nonlinear filtering methods for a large class of nonlinear wave equations that arise in applications such as quantum dynamics and laser generation and propagation in a unified framework. We consider…
A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be…
Motivated by the prevalence of non-smooth, possibly non-periodic signals in real-world applications, the output regulation of linear systems subject to non-smooth non-periodic exogenous signals has emerged as a challenging problem. A…
This paper is devoted to studying a type of logarithmic wave equation in non-cylindrical domains. Firstly, by the penalty method, we prove the existence of weak solutions to such kind of equations. Secondly, different from the dissipative…
In this manuscript we prove global existence and linear asymptotic behavior of small solutions to nonlinear wave equations. We assume that the quadratic part of the nonlinearity satisfies a non-resonant condition which is a generalization…
We address justification and solitary wave solutions of the cylindrical KdV equation which is formally derived as a long wave approximation of radially symmetric waves in a two-dimensional nonlinear dispersive system. For a regularized…
We study the evolution equations for gravitational waves, which are derived using the full metric to raise and lower indices. This method ensures full consistency between the Ricci tensor and all gauge restrictions and requirements, and…
This article concerns the time growth of Sobolev norms of classical solutions to the 3D quasi-linear wave equations with the null condition.
Using renormalization group techniques, we derive an extended short- pulse equation as approximation to a nonlinear wave equation. We investigate the new equation numerically and show that the new equation captures efficiently higher- order…
The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry, of differential equations is introduced. It is shown that the derivation of nonclassical symmetries for differential equations can…
We consider the two-dimensional quasilinear wave equations with quadratic nonlinearities. We introduce a new class of null forms and prove uniform boundedness of the highest order norm of the solution for all time. This class of null forms…
Nonlinear waves in a liquid containing gas bubbles are considered in the three-dimensional case. Nonlinear evolution equation is given for description of long nonlinear pressure waves. It is shown that in the general case the equation is…
We evaluate one-dimensional representations of quantum symmetric conjugacy classes of classical matrix groups along with their quantum stabilizer subgroups.
We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.
Two different versions of cubic sixth-order generalised Boussinesq-type wave equations are considered in this study. A generalised perturbation reduction method is used to solve these equations, which allows the reduction of considered…