相关论文: Approximate Analytical Solution for the Dynamic Mo…

The variational static formulation contributed in [International Journal of Engineering Science 143, 73-91 (2019)] is generalized in the present paper to model axial and flexural dynamic behaviors of elastic nano-beams by nonlocal strain…

This work comes as the second part in a series of investigations into the dynamics of rotating waves as solutions to lattice dynamical systems. Such nonlinear waves as solutions to mathematical equations are of great interest throughout the…

A formal uniform asymptotic solution of the system of differential equations $ h^{2}\frac{d^{2}U_{1}}{dz^{2}}+\Phi_{1} U_{1}=\alpha U_{2} $ , $ h^{2}\frac{d^{2}U_{2}}{dz^{2}}+\Phi_{2} U_{2}=\alpha U_{1}$ , for $ z\in D$ and for h real,…

We report nonlinear vibration localisation in a system of two symmetric weakly coupled nonlinear oscillators. A two degree-of-freedom model with piecewise linear stiffness shows bifurcations to localised solutions. An experimental…

We propose a natural gradient term for a class of second-order partial differential equations of the form \begin{equation}\nonumber M(x,Du,D^2u)+g(u)N(x,Du, D^2u)+f(x,u)=0 \;\;\mbox{in}\;\; \Omega, \end{equation} where…

By a mapping to the bosonic string theory, we present an exact solution to the O(26) sigma model coupled to 2-D quantum gravity. In particular, we obtain the exact gravitational dressing to the various matter operators classified by the…

A uniform bounded variation estimate for finite volume approximations of the nonlinear scalar conservation law $\partial_t \alpha + \mathrm{div}(\boldsymbol{u}f(\alpha)) = 0$ in two and three spatial dimensions with an initial data of…

We apply a recently proposed approximation method to the evaluation of non-Gaussian integral and anharmonic oscillator. The method makes use of the truncated perturbation series by recasting it via the modified Laplace integral…

We prove existence of variational solutions for a class of doubly nonlinear nonlocal evolution equations whose prototype is the double phase equation \begin{align*} \partial_t u^m &+ \text{P.V.}\int_{\mathbb{R}^N}…

We asymptotically derive a non-linear Langevin-like equation with non-Gaussian white noise for a wide class of stochastic systems associated with multiple stochastic environments, by developing the expansion method in our previous paper [K.…

This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…

In this paper, we study a class of quasilinear Schr\"{o}dinger equation of the form $$-\varepsilon^2\Delta u+V(x)u-\varepsilon^2(\Delta(|u|^{2\alpha}))|u|^{2\alpha-2}u &=&\lambda|u|^{q-2}u+|u|^{2^*(2\alpha)-2}u,\quad\mbox{in}{\mathbb{R}}^N,…

In this paper we study quasiconcavity properties of solutions of Dirichlet problems related to modified nonlinear Schr\"odinger equations of the type $$-{\rm div}\big(a(u) \nabla u\big) + \frac{a'(u)}{2} |\nabla u|^2 = f(u) \quad \hbox{in…

We develop computer-assisted tools to study semilinear equations of the form \begin{equation*} -\Delta u -\frac{x}{2}\cdot \nabla{u}= f(x,u,\nabla u) ,\quad x\in\mathbb{R}^d. \end{equation*} Such equations appear naturally in several…

In this paper, without any assumption on $v$ and under extremely mild assumption $u(x)=O(|x|^{K})$ at $\infty$ for some $K\gg1$ arbitrarily large, we prove classification of solutions to the following conformally invariant system with mixed…

We consider nonlinear filters for diffusion processes when the observation and signal noises are small and of the same order. As the noise intensities approach zero, the nonlinear filter can be approximated by a certain variational problem…

Analytical solution of the homoclinic orbit of a two dimensional system of differential equations that describes the hamiltonian part of the slow flow of a three degree of freedom dissipative system of linear coupled oscillators with an…

We study a new type of large-scale instability, which arises in obliquely rotating stratified electroconductive fluid with an external uniform magnetic field and a small-scale external force having zero helicity. This force gives rise to…

Let $(M^n,g)$ be an n-dimensional complete Riemannian manifold. We consider gradient estimates and Liouville type theorems for positive solutions to the following nonlinear elliptic equation: $$\Delta u+au\log u=0,$$ where $a$ is a nonzero…

In this Series, we study the weakly nonlinear dynamics of chemically active particles near the threshold for spontaneous motion. In this part, we focus on steady solutions and develop an `adjoint method' for deriving the nonlinear amplitude…