Nonlinear scalar field equation with competing nonlocal terms <sup>*</sup>

نویسندگان

چکیده

We find radial and nonradial solutions to the following nonlocal problem $$-\Delta u +\omega u= \big(I_\alpha\ast F(u)\big)f(u)-\big(I_\beta\ast G(u)\big)g(u) \text{ in } \mathbb{R}^N$$ under general assumptions, spirit of Berestycki Lions, imposed on $f$ $g$, where $N\geq 3$, $0\leq \beta \leq \alpha0$, then we deal two competing terms modelling attractive repulsive interaction

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Pattern formation in the nonlinear Schrödinger equation with competing nonlocal nonlinearities

We study beam propagation in the framework of the nonlinear Schrödinger equationwith competing Gaussian nonlocal nonlinearities. We demonstrate that such system can give rise to self-organization of light into stable states of trains or hexagonal arrays of laments, depending on the transverse dimensionality. This long-range ordering can be achieved bymere unidirectional beampropagation. We disc...

متن کامل

Integrable nonlocal nonlinear Schrödinger equation.

A new integrable nonlocal nonlinear Schrödinger equation is introduced. It possesses a Lax pair and an infinite number of conservation laws and is PT symmetric. The inverse scattering transform and scattering data with suitable symmetries are discussed. A method to find pure soliton solutions is given. An explicit breathing one soliton solution is found. Key properties are discussed and contras...

متن کامل

Chaoticons described by nonlocal nonlinear Schrödinger equation

It is shown that the unstable evolutions of the Hermite-Gauss-type stationary solutions for the nonlocal nonlinear Schrödinger equation with the exponential-decay response function can evolve into chaotic states. This new kind of entities are referred to as chaoticons because they exhibit not only chaotic properties (with positive Lyapunov exponents and spatial decoherence) but also soliton-lik...

متن کامل

Numerical solution of nonlinear elliptic equation with nonlocal condition ∗

Regimantas Čiupaila, Mifodijus Sapagovas, Olga Štikonienė Vilnius Gediminas Technical University Saulėtekio ave. 11, LT-10223 Vilnius, Lithuania [email protected] Institute of Mathematics and Informatics, Vilnius University Akademijos str. 4, LT-08663 Vilnius, Lithuania [email protected] Vilnius University Naugarduko str. 24, LT-03225 Vilnius, Lithuania olga.stikoniene@mif...

متن کامل

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota's bilinear method. Like the nonlocal NLS equation, th...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Nonlinearity

سال: 2021

ISSN: ['0951-7715', '1361-6544']

DOI: https://doi.org/10.1088/1361-6544/ac0d47