Related papers: Symmetric solutions of evolutionary partial differ…
Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related…
We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
Quasilinear (and semilinear) parabolic problems of the form $v'=A(v)v+f(v)$ with strict inclusion $\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$ of the domains of the function $v\mapsto f(v)$ and the quasilinear part $v\mapsto A(v)$ are…
In this work, we consider a system of multidimensional wave equations coupled by velocities with one localized fractional boundary damping. First, using a general criteria of Arendt- Batty, by assuming that the boundary control region…
We give a complete point-symmetry classification of all third-order evolution equations of the form $u_t=F(t,x,u,u_x, u_{xx})u_{xxx}+G(t,x,u,u_x, u_{xx})$ which admit semi-simple symmetry algebras and extensions of these semi-simple Lie…
This work is devoted to establishing the local-in-time well-posedness of strong solutions to the three-dimensional compressible primitive equations of atmospheric dynamics. It is shown that strong solutions exist, unique, and depend…
It is known that solutions of nonlocal dispersal evolution equations do not become smoother in space as time elapses. This lack of space regularity would cause a lot of difficulties in studying transition fronts in nonlocal equations. In…
We consider an abstract nonlinear second order evolution equation, inspired by some models for damped oscillations of a beam subject to external loads or magnetic fields, and shaken by a transversal force. When there is no external force,…
Dynamical simulations are a fundamental tool for studying the secular evolution of disc galaxies. Even at their maximum resolution, they still follow a limited number of particles and typically resolve scales of the order of a few tens of…
The generalized time-dependent harmonic oscillator is studied. Though several approaches to the solution of this model have been available, yet a new approach is presented here, which is very suitable for the study of cyclic solutions and…
Symmetry invariant local interaction of a many body system leads to global constraints. We obtain explicit forms of the global macroscopic condition assuring that at the microscopic level the evolution respects the overall symmetry.
This paper is devoted to the study of propagation dynamics for a large class of non-monotone evolution systems. In two directions of the spatial variable, such a system has two limiting systems admitting the spatial translation invariance.…
Existing methods rarely capture the temporal evolution of solution norms in vector nonlinear DDEs with variable delays and coefficients, often leading to overly conservative boundedness and stability criteria. We develop a framework that…
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
A symplectic, symmetric, second-order scheme is constructed for particle evolution in a time-dependent field with a fixed spatial step. The scheme is implemented in one space dimension and tested, showing excellent adequacy to experiment…
A natural example of evolution can be described by a time-dependent two degrees-of-freedom Hamiltonian. We choose the case where initially the Hamiltonian derives from a general cubic potential, the linearised system has frequencies 1 and…
For systems of partial differential equations in three spatial dimensions, dynamical conservation laws holding on volumes, surfaces, and curves, as well as topological conservation laws holding on surfaces and curves, are studied in a…
The dynamical symmetry breaking associated with the existence and non-existence of breather solutions is studied. Here, nonlinear hyperbolic evolution equations are calculated using a high-precision numerical scheme. %%% First, for…
We process snapshots of trajectories of evolution equations with intrinsic symmetries, and demonstrate the use of recently developed eigenvector-based techniques to successfully quotient out the degrees of freedom associated with the…