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Existence and stability of PT-symmetric gap solitons in a periodic structure with defocusing nonlocal nonlinearity are studied both theoretically and numerically. We find that, for any degree of nonlocality, gap solitons are always unstable…

Pattern Formation and Solitons · Physics 2018-11-07 Chandroth P. Jisha , Alessandro Alberucci , Valeriy A. Brazhnyi , Gaetano Assanto

In the present paper we consider an optical system with a $\chi^{(2)}$-type nonlinearity and unspecified $\mathcal{PT}$-symmetric potential functions. Considering this as an inverse problem and positing a family of exact solutions in terms…

Pattern Formation and Solitons · Physics 2015-01-06 Y. N. Truong Vu , J. D'Ambroise , P. G. Kevrekidis , F. Kh. Abdullaev

We consider the one-dimensional nonlinear Schr\"odinger equation with focusing, power nonlinearity, and a repulsive delta potential. We show that if the potential is not too strong, the construction by Nguy\~{\^e}n (2019) of solutions…

Analysis of PDEs · Mathematics 2023-10-16 Stephen Gustafson , Takahisa Inui

By using the Darboux transformation, we obtain two new types of exponential-and-rational mixed soliton solutions for the defocusing nonlocal nonlinear Schrodinger equation. We reveal that the first type of solution can display a large…

Exactly Solvable and Integrable Systems · Physics 2019-11-20 Tao Xu , Sha Lan , Min Li , Ling-Ling Li , Guo-Wei Zhang

We consider a class of one dimensional Vector Nonlocal Non-linear Schr\"odinger Equation (VNNLSE) in an external complex potential with time-modulated Balanced Loss-Gain(BLG) and Linear Coupling(LC) among the components of Schr\"odinger…

Exactly Solvable and Integrable Systems · Physics 2023-11-01 Supriyo Ghosh , Pijush K. Ghosh

The nonlinear Schr{\"o}odinger (NLS) equation, which incorporates higher-order dispersive terms, is widely employed in the theoretical analysis of various physical phenomena. In this study, we explore the non-commutative extension of the…

Mathematical Physics · Physics 2023-11-13 H. W. A. Riaz , J. Lin

We discuss the stability properties of the solutions of the general nonlinear \Schrodinger\ equation (NLSE) in 1+1 dimensions in an external potential derivable from a parity-time ($\PT$) symmetric superpotential $W(x)$ that we considered…

Pattern Formation and Solitons · Physics 2017-12-06 John F. Dawson , Fred Cooper , Avinash Khare , Bogdan Mihaila , Edward Arevalo , Ruomeng Lan , Andrew Comech , Avadh Saxena

The integrable focusing nonlinear Schrodinger equation admits soliton solutions whose associated spectral data consist of a single pair of conjugate poles of arbitrary order. We study families of such multiple-pole solitons generated by…

Analysis of PDEs · Mathematics 2021-08-05 Deniz Bilman , Robert Buckingham , Deng-Shan Wang

We study noise-induced perturbations of dispersion-managed solitons by developing soliton perturbation theory for the dispersion-managed nonlinear Schroedinger (DMNLS) equation, which governs the long-term behavior of optical fiber…

Pattern Formation and Solitons · Physics 2009-11-13 Jinglai Li , Elaine Spiller , Gino Biondini

The well-known (1+1D) nonlinear Schr\"odinger equation (NSE) governs the propagation of narrow-band pulses in optical fibers and others one-dimensional structures. For exploration the evolution of broad-band optical pulses (femtosecond and…

Optics · Physics 2016-12-26 D. Dakova , A. Dakova , V. Slavchev , L. Kovachev

We investigate exact travelling wave solutions of higher order nonlinear Schrodinger equation in the absence of third order dispersion, which exhibit non-trivial self phase modulation. It is shown that, the corresponding dynamical equation,…

Pattern Formation and Solitons · Physics 2011-06-01 Anshul Saini , Vivek M. Vyas , S. N. Pandey , T. Solomon Raju , Prasanta K. Panigrahi

In this paper we perform a numerical study on the interesting phenomenon of soliton reflection of solid walls. We consider the 2D nonlinear Schrodinger equation as the underlying mathematical model and we use an implicit-explicit type…

Numerical Analysis · Mathematics 2016-09-09 Theodoros Katsaounis , Dimitrios Mitsotakis

In this paper we deal with a nonlinear Schr\"{o}dinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time…

Quantum Physics · Physics 2015-05-14 W. B. Cardoso , S. A. Leao , A. T. Avelar , D. Bazeia , M. S. Hussein

We obtain novel periodic as well as hyperbolic solutions of an Ablowitz-Musslimani variant of the coupled nonlocal, nonlinear Schr\"odinger equation (NLS) as well as a coupled nonlocal modified Korteweg-de Vries (mKdV) equation which can be…

Pattern Formation and Solitons · Physics 2022-09-16 Avinash Khare , Avadh Saxena

In this work, we numerically consider the initial value problem for nonlinear Schr\"odinger (NLS) type models arising in the physics of ultracold boson gases, with generic Gaussian wavepacket initial data. The corresponding Gaussian's width…

Pattern Formation and Solitons · Physics 2016-09-08 E. G. Charalampidis , J. Cuevas-Maraver , D. J. Frantzeskakis , P. G. Kevrekidis

We discuss existence and stability of two-dimensional solitons in media with spatially nonlocal nonlinear response. We show that such systems, which include thermal nonlinearity and dipolar Bose Einstein condensates, may support a variety…

Pattern Formation and Solitons · Physics 2007-05-23 S. Skupin , O. Bang , D. Edmundson , W. Krolikowski

We investigate the large-space and large-time asymptotic behavior of a soliton gas for the focusing nonlinear Schr\"odinger equation. The soliton gas is constructed as the continuum limit of pure $N$-soliton solutions as $N\to\infty$, with…

Exactly Solvable and Integrable Systems · Physics 2026-05-21 Dedi Yan , Xianguo Geng , Wei Jiao

We have performed numerical analysis of the two-dimensional (2D) soliton solutions in Bose-Einstein condensates with nonlocal dipole-dipole interactions. For the modified 2D Gross-Pitaevski equation with nonlocal and attractive local terms,…

Pattern Formation and Solitons · Physics 2015-06-26 V. M. Lashkin

The numerical solutions of nonlocal and local Boltzmann kinetic equations for the simulation of peripheral and central heavy ion reactions are compared. The experimental finding of enhancement of mid-rapidity matter shows the necessity to…

Nuclear Theory · Physics 2007-05-23 Klaus Morawetz

The nonlinear coupling between the light beams and non-resonant ion density perturbations in a plasma is considered, taking into account the relativistic particle mass increase and the light beam ponderomotive force. A pair of equations…

Pattern Formation and Solitons · Physics 2009-11-07 P. K. Shukla , R. Fedele , M. Onorato , N. L. Tsintsadze