相关论文: Construction of quasi-periodic solutions for delay…

We prove the existence of almost-periodic solutions for quasi-linear perturbations of the Airy equation. This is the first result about the existence of this type of solutions for a quasi-linear PDE. The solutions turn out to be analytic in…

By applying the Craig-Wayne-Bourgain (CWB) method, we establish the persistence of periodic solutions to multi-dimensional nonlinear wave equations (NLW) with unbounded perturbation.

The paper [Shi19] uses the Craig-Wayne-Bourgain method to construct solutions of an elliptic problem involving parameters. The results of [Shi19] include regularity assumptions on the perturbation and involve excluding parameters. The paper…

By applying the Craig-Wayne-Bourgain (CWB) method, we establish the existence of periodic response solutions to multi-dimensional nonlinear Schr\"{o}dinger equations (NLS) with unbounded perturbation.

We investigate the persistency of quasi-periodic solutions to multi-dimensional nonlinear Schr\"{o}dinger equations (NLS) involving Gevrey smooth nonlinearity with an arbitrary Gevrey index $\alpha>1$. By applying the Craig-Wayne-Bourgain…

We construct multi-phase travelling waves which are periodic in time and quasi-periodic in the spatial variable for infinite nonlinear chains with nearest neighbor interactions. The main difficulty in the construction is a small divisor…

In this paper, we present an averaging method for obtaining quasi-periodic response solutions in perturbed, real analytic, quasi-periodic systems with Diophantine frequency vectors. Under the assumptions that the averaged system possesses a…

Symplectic integrators are the established standard for long-term simulations of nearly-integrable Hamiltonian systems due to their preservation of geometric structures. However, they suffer from an inherent limitation: secular phase-shift…

By exploiting a recently developed connection between Heun's differential equation and the generalized associated Lam\'e equation, we not only recover the well known periodic solutions, but also obtain a large class of new, quasi-periodic…

Component Mode Synthesis methods, such as the Craig-Bampton (CB) approach, are widely used in structural dynamics due to their modularity and compatibility with substructuring workflows. While highly effective for linear systems, extending…

This work focuses on the existence of quasi-periodic solutions for ordinary and delay differential equations (ODEs and DDEs for short) with an elliptic-type degenerate equilibrium point under quasi-periodic perturbations. We prove that…

Two combined methods for computing solutions of time-varying semilinear differential-algebraic equations (descriptor systems) are obtained. When constructing the methods, time-varying spectral projectors which can be found numerically are…

In this paper, we study the nonlinear dispersive waves including the rarefaction and dispersive shock waves in the discrete modified KdV equation through the numerical simulations of the dispersive Riemann problems. In particular, we…

We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…

In this article, we systematically explain how to apply the analytical technique called the invariant subspace method to find various types of analytical solutions for a coupled nonlinear time-fractional system of partial differential…

A linearized numerical scheme is proposed to solve the nonlinear time fractional parabolic problems with time delay. The scheme is based on the standard Galerkin finite element method in the spatial direction, the fractional Crank-Nicolson…

We extend the piecewise orthogonal collocation method to computing periodic solutions of coupled renewal and delay differential equations. Through a rigorous error analysis, we prove convergence of the relevant finite-element method and…

This paper proposes a domain decomposition subspace neural network method for efficiently solving linear and nonlinear partial differential equations. By combining the principles of domain decomposition and subspace neural networks, the…

The paper develops the method for construction of the families of particular solutions to the nonlinear Partial Differential Equations (PDE) without relation to the complete integrability. Method is based on the specific link between…

A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…