Related papers: Modulation Spaces and Nonlinear Evolution Equation…
We show upper and lower embeddings of $\alpha_1$-modulation spaces in $\alpha_2$-modulation spaces for $0 \leq \alpha_1 \leq \alpha_2 \leq 1$, and prove partial results on the sharpness of the embeddings.
In this paper, under an abstract setting we establish the spreading properties and the existence, non-existence and global attractivity of spatially heterogeneous steady states for a large class of monotone evolution systems without the…
We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…
In this paper, we consider group classification of local and quasi-local symmetries for a general fourth-order evolution equations in one spatial variable. Following the approach developed by Zhdanov and Lahno, we construct all inequivalent…
Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological systems under increased environmental pressure. We here…
Discusses several integrability tests for nonlinear evolution equations.
We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations with a polynomially growing quasi-monotone nonlinearity and multiplicative Poisson noise. We also study existence and uniqueness of…
We start a study of various nonlinear PDEs under the effect of a modulation in time of the dispersive term. In particular in this paper we consider the modulated non-linear Schr\"odinger equation (NLS) in dimension 1 and 2 and the…
Given a nonlinear evolution equation in (1+n) dimensions, which has spatially extended traveling wave solutions, it can be extended into a system of two coupled equations, one of which generates the original traveling waves, and the other…
Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with…
After defining classical weighted modulation spaces we show some basic properties. In this work we additionally choose an approach in terms of the frequency-uniform decomposition and a discussion on the weights of modulation spaces leads to…
An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…
We put forward new properties of lattice solitons in materials and geometries where both, the linear refractive index and the nonlinearity are spatially modulated. We show that the interplay between linear and out-of-phase nonlinear…
Evolution is simultaneously driven by a number of processes such as mutation, competition and random sampling. Understanding which of these processes is dominating the collective evolutionary dynamics in dependence on system properties is a…
In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on Banach space with locally monotone operators, which is a generalization of the classical result by J.L. Lions for monotone operators.…
The most general local Markovian stochastic model is investigated, for which it is known that the evolution equation is the Fokker-Planck equation. Special cases are investigated where uncorrelated initial states remain uncorrelated.…
A class of solvable (systems of) nonlinear evolution PDEs in multidimensional space is discussed. We focus on a rotation-invariant system of PDEs of Schr\"odinger type and on a relativistically-invariant system of PDEs of Klein-Gordon type.…
Nonlocal symmetries for exactly integrable two-field evolutionary systems of the third order have been computed. Differentiation of the nonlocal symmetries with respect to spatial variable gives a few nonevolutionary systems for each…
This paper presents a mathematical foundation for physical models in nonlinear optics through the lens of evolutionary equations. It focuses on two key concepts: well-posedness and exponential stability of Maxwell equations, with models…
Obstacles to integrability in perturbed evolution equations are overcome by allowing higher-order terms in the expansion of the solution to depend explicitly on time and position. With a special expansion algorithm, obstacles vanish…