We show the existence of a nontrivial solution for a class of the systems of the superquadratic nonlinear wave equations with Dirichlet boundary conditions and periodic conditions with a superquadratic nonlinear terms at infinity which have continuous derivatives. We approach the variational method and use the critical point theory which is the Linking Theorem for the strongly indefinite corres...

We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finitetime trajectory of a nonlinear dynamical system can be loaded approximately into the initial condition of a linear delay-differential system. It is further shown that the initial condition can be extended to a periodic solution of the delay-differential syst...

In this paper, applying He’s energy balance method to determine frequency formulation relations of nonlinear oscillators with discontinuous term or fractional potential. By calculation and computer simulations, compared with the exact solutions show that the results obtained are of high accuracy. Keywords—He’s energy balance method; Periodic solution; Nonlinear oscillator; Discontinuous; Fracti...

In this paper, we consider variform exact peakon solutions for four nonlinear wave equations. We show that under different parameter conditions, one nonlinear wave equation can have different exact one-peakon solutions and different nonlinear wave equations can have different explicit exact one-peakon solutions. Namely, there are various explicit exact one-peakon solutions, which are different ...

A normal form is derived for Hamiltonian–Hopf bifurcations of solitary waves in nonlinear Schrödinger equations with general external potentials. This normal form is a simple second-order nonlinear ordinary differential equation (ODE) that is asymptotically accurate in describing solution dynamics near Hamiltonian–Hopf bifurcations. When the nonlinear coefficient in this normal form is complex,...

By employing the contraction mapping principle and applying Gronwall-Bellman's inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solution for nonlinear impulsive delay model of hematopoiesis.

In the present investigation, breathers and rogue waves on double-periodic background are successfully constructed by Darboux transformation using a plane wave seed solution. Firstly, for reverse-space-time derivative nonlinear Schrödinger equation is constructed. Secondly, periodic solutions, breathers, derived n-fold transformation. Thirdly, higher-order semi-degenerate addition, dynamic beha...

Sufficient conditions for the existence of at least one solution of anti-periodic boundary value problems for nonlinear functional difference equations are established. We allow f to be at most linear, superlinear or sublinear in obtained results.

We obtain exact moving breather solutions of a generalized discrete nonlinear Schrödinger equation. For finite lattices, we find two different moving periodic breather solutions while for an infinite lattice we find a localized moving breather solution.

A modal-based model of milling machine tools subjected to time-periodic nonlinear cutting forces is introduced. The model describes the phenomenon of bistability for certain cutting parameters. In engineering, these parameter domains are referred to as unsafe zones, where steady-state milling may switch to chatter for certain perturbations. In mathematical terms, these are the parameter domains...