相关论文: Superposed periodic kink and pulse solutions of co…

The nonlinear Schroedinger equation is studied for a periodic sequence of delta-potentials (a delta-comb) or narrow Gaussian potentials. For the delta-comb the time-independent nonlinear Schroedinger equation can be solved analytically in…

Landen formulas, which connect Jacobi elliptic functions with different modulus parameters, were first obtained over two hundred years ago by making a suitable quadratic transformation of variables in elliptic integrals. We obtain and…

In this paper, the trial function method is employed to find the exact solutions for high-order nonlinear Schr\"odinger equations with time-dependent coefficients. This system describes the propagation of ultrashort light pulses in…

An analytical solution to the nonlinear differential equation describing the equation of motion of a particle moving in an unforced physical system with linear damping, governed by a cubic potential well, is presented in terms of the Jacobi…

We consider the Novikov problem, namely, the problem of describing the level lines of quasiperiodic functions on the plane, for a special class of potentials that have important applications in the physics of two-dimensional systems.…

In a recent paper Zhang and Li have doubted our claim that whenever a nonlinear equation has solutions in terms of the Jacobi elliptic functions $\cn(x,m)$ and $\dn(x,m)$, then the same nonlinear equation will necessarily also have…

A novel method is developed for constructing periodic solutions of a model equation describing nonlocal Josephson electrodynamics. This method consists of reducing the equation to a system of linear ordinary differential equations through a…

It is shown that the tight-binding approximation of the nonlinear Schr\"odinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear…

We develop a general mapping from given kink or pulse shaped travelling-wave solutions including their velocity to the equations of motion on one-dimensional lattices which support these solutions. We apply this mapping - by definition an…

We deal with the existence of $2\pi$-periodic solutions to the following non-local critical problem \begin{equation*} \left\{\begin{array}{ll} [(-\Delta_{x}+m^{2})^{s}-m^{2s}]u=W(x)|u|^{2^{*}_{s}-2}u+ f(x, u) &\mbox{in} (-\pi,\pi)^{N} \\…

In this paper we continue the work that we began in arXiv:1912.07537. Given $1<p<N$, two measurable functions $V\left(r \right)\geq 0$ and $K\left(r\right)> 0$, and a continuous function $A(r) >0\ (r>0)$, we consider the quasilinear…

We propose an integrable system of coupled nonlinear Schrodinger equations with cubic-quintic terms describing the effects of quintic nonlinearity on the ultra-short optical soliton pulse propagation in non-Kerr media. Lax pair, conserved…

We study the existence of a periodic solution for a differential equation with distributed delay. It is shown that, for a class of distributed delay diferential quations, a symmetric period 2 solution, where the period is twice the maximum…

We show that the generalised nonlinear Schr\"{o}dinger equation (GNLSE) with quartic dispersion supports infinitely many multipulse solitons for a wide parameter range of the dispersion terms. These solitons exist through the balance…

Two-place nonlocal systems have attracted many scientists' attentions. In this paper, two-place non-localities are extended to multi-place non-localities. Especially, various two-place and four-place nonlocal nonlinear Schrodinger (NLS)…

We derive two new solutions in terms of elliptic functions, one for the dark and one for the bright soliton regime, for the semi-discrete cubic nonlinear Schroedinger equation of Ablowitz and Ladik. When considered in the complex plane,…

Quasi-periodic solutions of a nonlinear periodic polyharmonic equation in $\R^n$, $n>1$, are studied. It is proven that there is an extensive "non-resonant" set ${\mathcal G}\subset \R^n$ such that for every $\vec k\in \mathcal G$ there is…

We consider the nonlinear Schr\"odinger equation on a compact manifold near an elliptic periodic geodesic. Using a geometric optics construction, we construct quasimodes to a nonlinear stationary problem which are highly localized near the…

We prove the existence of infinitely many nontrivial weak periodic solutions for a class of fractional Kirchhoff problems driven by a relativistic Schr\"odinger operator with periodic boundary conditions and involving different types of…

Landen transformation formulas, which connect Jacobi elliptic functions with different modulus parameters, were first obtained over two hundred years ago by changing integration variables in elliptic integrals.We rediscover known results as…